Why the search for particle dark matter is hopeless, part 1

Previously, I made a list of five criteria for a convincing dark matter detection. I discussed the first four, which I hope are obvious to everyone who works in the field, but it seemed worthwhile to write them out explicitly given the hint of a detection by LZ. I left the fifth criterion – that whatever the dark matter is it should naturally explain the observed MONDian phenomenology – to be discussed separately, so that’s what we’ll do here.

Explaining the observed MONDian phenomenology is a high bar. That it does not follow naturally from dark matter should be obvious. It used to be, but apparently it no longer is, so let’s think it through. Indeed, it’s going to take two posts to get through.

First, some definitions:

Cold Dark Matter (CDM): the non-relativistic, non-baryonic dark matter that is standard to cosmology. Usually presumed to be a WIMP, it could in principle be any mass that is slow-moving and does not participate in big bang nucleosynthesis. I will nevertheless assume, as the vast majority of scientists do, that it is some new particle, if not necessarily a WIMP.

Generic Dark Matter (DM): could be any unseen mass, but here I will use it to mean non-WIMP particle DM candidates that don’t necessarily do what pure CDM predicts. For example, warm (WDM) or self-interacting dark matter (SIDM) might produce cored rather than cuspy dark matter halos. So by generic DM I mean any new particle that doesn’t interact with baryons except through gravity. This is pretty much everything that is commonly discussed in particle physics, with only a few obscure exceptions. Cold dark matter is of course a subset of generic DM, but it makes specific predictions, like cuspy halos, while generic DM is just there adding mass.

Modified Newtonian Dynamics (MOND): the hypothesis that the effective force law at low accelerations $a \ll a_0 = 1.2 \times 10^{-10}\,\mathrm{m}\,\mathrm{s}^{-2}$ becomes $a \rightarrow \sqrt{a_0\,g_N}$ , where $g_N$ is the acceleration predicted by Newton ( $g_N = GM/r^2$ for a point mass M; more generally one must solve the Poison equation for the observed mass distribution). The Newtonian and MOND regimes are connected by an interpolation function $\nu$ so that $a = \nu(g_N/a_0)\, g_N$ . The interpolation function is not fundamental and only matters around the transition $a \approx a_0$ .

Data wanting explanation

OK, so let’s see how these compare with galaxy data. I’m only going to talk about galaxy data because I’ve talked about everything else in other posts, and to offer a reflection of those who think CMB data are the only form of evidence that matters, to the exclusion of any other contrary evidence. If we adopt the same attitude, then galaxy data already suffice to falsify DM. Note my use of the generic DM there, not just CDM.

So what do we need to understand about galaxies? Their many regularities, as summarized in this table along with whether each of CDM, generic DM, and MOND provide a satisfactorily explanation:

Observation	[L]CDM	Generic DM	MOND
Flat rotation curves	No	Sure	By construction
Inner rotation curve shapes maximal disks & diversity	No	Maybe?	Yes
Stellar Mass-to-Light Ratios	No	whatever	Yes
Baryonic Tully-Fisher Relation	No	No	Yes
Radial Acceleration Relation	No	No	Yes
Central Surface Density Relation	No	No	Yes
Renzo’s Rule (Sancisi’s Law)	No	Maybe? but no, not really	Yes
Acceleration scale	LOL no, CDM is scale free	No	Yes

Satisfactory is doing a lot of work in evaluating whether each case provides a satisfactory explanation. It is easy to find claims in the literature to explain some if not all of these items, but these claims are generally not satisfactory. From the perspective of the current sociology of the field, they don’t need to be: as long as someone asserts that [insert observation] works in [C]DM, the community hears what it wants to hear, mentally checks the box, and files it under “not a problem” even when it remains very much a problem.

Rotation curve shapes: flat far out; baryon-like near-in

I’ve written about all of these things at one point or another here, but for starters, let’s consider flat rotation curves. Flat rotation curves were, of course, a primary reason why we invoked dark matter in the first place. Dark matter can certainly explain flat rotation curves at the level of “anything in excess of the baryonic rotation curve is attributable to dark matter.” This is exactly what generic DM was initially invoked to do. Part and parcel of this early construction was that dark matter was not needed at small radii. For the bright galaxies studied in the ’70s and early ’80s, the stars explained the inner parts of rotation curves quite well, a condition dubbed “maximum disk.” The inner regions were star-dominated, and dark matter only became relevant far out. That’s why I’ve given generic DM a “sure” grade: that’s what it was invoked to do.

The rotation curve (data points) of the high surface brightness spiral galaxy NGC 7331. The blue line is the Newtonian prediction for the observed stars and gas. This disk is maximal, meeting the rotation curve data at small radii *for a stellar population mass-to-light ratio* of $0.42\;M_{\odot}/L_{\odot}$ at [3.6] microns. (Nominally we expect a typical value of 0.5 in this band, so maximum disk here is already a bit on the low side in terms of stellar populations: there isn’t much leeway to decrease this further as would be necessary to accommodate a cuspy dark matter halo.) Despite the good match at small radii, the need for something extra, be it dark matter or MOND, becomes increasingly clear further out.

It is a low bar to say “any dynamical mass that’s not luminous is dark.” This, by itself, is not a satisfactory explanation: it is just an inference that when what we see falls short, then DM makes up the rest. To become a satisfactory explanation, one would need a theory that predicts this as an outcome. [L]CDM is better than generic DM in that it does make predictions.

CDM predicts NFW halos, at least when left to itself in dark matter-only simulations. These do not lead to flat rotation curves. NFW halos have rotation curves that rise steeply, turnover, then fall gradually. They are not flat over an extended region as routinely observed in real galaxies. In order to obtain the observed flatness requires a combination of baryons plus dark matter. That then requires a good theory for how the luminous galaxy forms, which is a lot more complicated than just an NFW halo. There are now lots of simulations that do this, but they generally don’t agree with each other, so we can’t claim to have a clear prediction from LCDM.

Despite their differences, detailed simulations of galaxy formation do share some common failure modes. Simulated galaxies tend to be too dark matter dominated so that (i) bright, high surface brightness objects often have submaximal disks, unlike real galaxies like NGC 7331 above or our own Milky Way. The shapes of simulated rotation curves tend to (ii) rise too fast relative to the data (those pesky cusps are hard to get rid of) and (iii) the outer rotation curves tend to fall too much, typically having a gradual decline rather than an extended flat portion. I say “tend to” and “typically” because there are a lot of simulations that share these failings, but the details differ from simulation to simulation.

I guess I should give an example. Here is a nice one from the SIMBA simulations:

**Figure 2** from Glowacki et al. (2020): Example galaxies from the SIMBA snapshots and their corresponding rotation curves. Galaxies have been selected to closely match galaxies in the THINGS survey, in stellar mass and SFR. Left side: the moment-0 maps for the H I , H₂, and stellar distributions for the galaxy. Three viewing angles are offered, along the x, y, and z-axis of the snapshot box. The color bars are in units of solar masses M_⊙. Right side: rotation curves, generated from the mass distribution of all particles making up the galaxy (giving the solid black curve), and alternatively from the velocity of the gas particles (dot–dashed blue curve).

This is good: it shows us the distribution of the component baryons by phase (atomic gas, molecular gas, and stars), and the total rotation curves*. I think these are good simulation results in that they provide a reasonable depiction of what we should expect in LCDM. They do not look like real galaxies.

Apparently they look close enough to pass casual inspection. They are qualitatively correct in that a lot of rotation curves for bright galaxies go up steeply, peak, then fall some to the flat portion (NGC 7331 is a typical example). However, the rotation curves of these simulated objects illustrate two of the three typical problems noted above: the disks are too submaximal (compare the green dashed lines to the blue line for NGC 7331) and their rotation curves fall too far before flattening out. Here the simulated rotation curves don’t really flatten out at all, a problem I’ve seen in other simulations, not just SIMBA. I find it remarkable that half a century after flat rotation curves helped found the dark matter paradigm, typical simulations in the standard model of cosmology routinely fail to satisfactorily reproduce this essential observational fact.

The third problem is that simulated rotation curves tend to rise too rapidly, which leads to the cusp-core problem. This problem is particularly pronounced in dwarf galaxies, but such low mass galaxies are not well resolved by most simulations. This issue is addressed by specialized, high resolution simulations like those described by Ruan et al. (2025), which I previously discussed in the context of Tully-Fisher. They do a good job of explaining the small scatter in the Tully-Fisher relation if you don’t look too closely into how that is accomplished. They also show example rotation curves, which exemplify the issue with the inner shape:

The rotation curve of simulated dwarf galaxy-like object r614 (red line) from the top panel of Fig. 2 of Ruan et al. (2025) compared to a real galaxy of similar mass, the low surface brightness galaxy F583-1 (data points).

The suite of simulations from which this example is drawn is one of the better ones in terms of making realistic-looking galaxy-like objects. They are descended from the family of simulations that first claimed to convert cusps into cores. That hasn’t worked out here: the rotation curve of simulated dwarf r614 looks exactly like a cuspy NFW halo. This is what LCDM generically predicts, but real galaxies don’t do that. [Same as it ever was – see Fig. 14 of McGaugh & de Blok (1998).]

Note that I am not saying the simulations are wrong. I think they often do a reasonable job of showing what we should expect for LCDM. What I am saying is that LCDM simulations don’t look like reality. If we believe the simulations get the predictions of LCDM right, then LCDM is falsified. If we don’t want to grant credence to that line of thought, then we either tweak our simulations in an effort to iterate towards something that looks less unrealistic, or simply ignore the uncomfortable aspects of the data. Those two approaches pretty much encompass the past thirty years of the field of galaxy formation.

Regardless of any notional improvements to future simulations, LCDM does not generically get flat rotation curves right – hence the “no” in the table above. I give generic DM a “sure” in this category because the bar is set lower. LCDM at least makes predictions, albeit filtered through the effects of baryonic feedback, which is treated differently by different simulations. There is no prediction for generic DM, so sure, whatever. To illustrate how low this bar is, consider the difference between fitting the data and predicting it. If presented with rotation curve data, we can fit it with any DM halo model you can imagine. In that process, we will reproduce the observed flatness by construction. That’s what a fit does. However, predicting the rotation curve is a much harder proposition. There is no reason to expect baryonic disk+DM halo to result in a flat rotation curve. Indeed, there is only a small sector of the available parameter space where that is the result; it is quite easy to build a plausible-seeming model that has either a rising or a declining rotation curve. I was surprised in my earliest modeling attempts to find just how unlikely the result was to be a flat rotation curve. Lots of subsequent simulations corroborate that without confronting the issue.

Note that MOND, like dark matter, was invented to explain flat rotation curves. That rotation curves are flat happens by construction; there is no evidentiary value in checking this box. Positive evidence does follow from more extended rotation curves than were known at the time of its invention. But aside from that relatively recent development, there’s not much to brag about in the first row of the table for any of the ideas listed there.

The different hypotheses do become distinguishable in the subsequent rows. MOND made specific, a priori predictions for the other entries in the table, and these were all realized by subsequent observations. This behavior, which I refer to collectively as the MOND phenomenology, was not anticipated by dark matter, and is not readily explained by it. Moreover, predictions matter. Even if we do come up with a DM explanation for each of the things MOND predicted a priori, why should we privilege the idea that failed to make the same predictions? This is the opposite of how science is supposed to work.

Rotation curve shapes

We’ve touched on the concept of maximum disk in bright spirals where the inner shape of the rotation curve is stipulated by the observed distribution of stars. This is not expected in LCDM, where the effects of cuspy halos and adiabatic compression combine to preclude disks from becoming maximal – hence the submaximal disks in SIMBA and other simulations. However, feedback can also play a role, so it is not entirely clear what the end results might be for high surface brightness galaxies. (The typical assertion from theory is that high mass galaxies have deep enough potential wells that the impact of feedback is minimal, but that leads to submaximal disks.)

Matters become simpler in low surface brightness galaxies, which are observed to be have large mass discrepancies. This dark matter domination extends to small radii; stellar mass has little influence on the dynamics. Consequently, one expects rotation curves to simply trace that of the dark matter halo. At a given mass, different DM-dominated galaxies reside in pretty much the same DM halo, so should have pretty much the same rotation curve. They do not.

Though long known observationally, this came as a surprise to the simulation community, who coined the term “diversity” to refer to it. They failed to notice that the diversity of rotation curve shapes correlates with the diversity of surface brightnesses: high surface brightness galaxies have rapidly rising rotation curves, low surface brightness galaxies have gradually rising rotation curves. The relation is so strong, it can be seen by eye:

*Rotation curves color coded by galaxy surface brightness*. There is an almost perfect rainbow variation that is plain to see: low surface brightness galaxies (blue tones) have gradually rising rotation curves; high surface brightness galaxies (red tones) have rapidly rising rotation curves – sometimes so fast that the flat velocity is already attained within 1 kpc. (Adapted from McGaugh 2020.)

The systematic variation of rotation curve shape with surface brightness is the signature of MOND. Lower surface brightness means lower stellar surface density means lower acceleration means a larger mass discrepancy. Low surface brightness galaxies are inferred to be dark matter dominated as a consequence. Though initially surprising from the conventional perspective, this is exactly what MOND predicted a priori. Milgrom discussed the expected variation in rotation curve shapes in his original series of papers. That’s what is observed above. I have not seen the same effect emerge from simulations, nor do I expect to.

Stellar population mass-to-light ratios

The mass of the stars matters to the dynamics. We observe starlight, but need to know the stellar mass for the physics. The connection between the two is encapsulated by the mass-to-light ratio of the stellar population.

Conventionally, constructing a model or fitting a rotation curve requires a minimum of three physical parameters: one for the stellar mass with its corresponding mass-to-light ratio, and two for the dark matter halo (typically a mass and length scale). That is more parameters than are required to describe the data, so there is considerable degeneracy between them. It’s like fitting a small number of points with a high order polynomial: a fit is not only guaranteed, but entire families of equally good fits are possible. Consequently, the precise value of the fitted stellar mass-to-light ratio does not provide a test; it can be whatever it needs to be and an appropriate halo fit can be obtained.

To fit a rotation curve in MOND, one has only knowledge of the RAR and a single physical^# parameter, the stellar mass-to-light ratio. That provides a test. If there is nothing to MOND beyond being a weird fitting formula, then the mass-to-light ratio is a free-floating parameter that will take whatever value is necessary to provide a fit. If instead it corresponds to physical reality, then the fitted stellar mass-to-light ratios should conform to astrophysical expectations for stellar populations.

The stellar mass-to-light ratios from MOND fits (points) in the blue (left panel) and near-infrared (right panel) pass-bands plotted against B-V color (bluer colors to the left, redder to the right). From the perspective of stellar populations, one expects more scatter and a steeper color dependence in the blue band, as observed. The lines are stellar population models from Bell et al. (2003). These are completely independent, and have not been fit to these data in any way. (Adapted from Famaey & McGaugh 2012).

We know a lot about stars and their evolution. It is possible to build extremely sophisticated stellar population models. These of course have their own uncertainties, but they are good enough to provide a clear expectation for what the stellar mass-to-light ratio should be. As the figure above illustrates, MOND fits return the correct amplitude for M_*/L and its variation with color. The expected amount of bandpass-dependent scatter is also apparent: more in the blue, less in the near-IR. One could not hope for better astrophysical agreement.

Tully-Fisher Relation

MOND correctly anticipated a number of striking features about the Tully-Fisher relation. People seem to obsess about the slope; MOND predicts $V_f \propto M_b^{1/4}$ while the dark matter halo version of this is $V_{200} \propto M_{200}^{1/3}$ . We observe the former. The latter isn’t a prediction for what we can see, so modeling is required. There exist many models, so there is no clear consensus on what LCDM predicts. It certainly didn’t predict $V_f \propto M_b^{1/4}$ , which I guess is why people obsess over this aspect of the observation and complain as the slope has converged to that value with increasing precision as the data have improved.

LCDM models that adhere to abundance matching naturally predict curvature in Tully-Fisher. This is a generic expectation that necessarily arises when mapping the curving shape of the galaxy luminosity function to the power law of the DM halo mass function. A representative example is provided by the model of Sales et al. (2017) (red line in plot). This model does OK for a range in mass, but departs from the data at both high and low mass ends.

The Baryonic Tully-Fisher relation for spiral galaxies (blue), gas rich dwarf irregulars (green), and Local Group galaxies (yellow). The straight black line is MOND. The curving red line is the model of *Sales et al. (2017)*. There are **many** *variations on the LCDM prediction while that of MOND works better and has remained unchanged since its introduction in 1983.*

There are other aspects of Tully-Fisher that are problematic for the dark matter picture. More concerning to me than the slope is the small scatter. If one goes through the exercise of tabulating the scatter budget, one finds that it should be large. There are many sources of potential variance, including that from halos themselves. At a given mass, halos should come in a range of concentrations; that by itself exceeds the observed scatter budget, which is entirely explained by the expected amount of scatter in the mass-to-light ratios of stellar populations.

Another prediction of MOND that sits uncomfortably with dark matter is the absence of second parameter effects. Newton says $V^2 = GM/R$ ; both mass and radius matter to the velocity. Yet radius is not observed to be relevant, only the mass, as predicted by MOND: $V_f^4 = a_0GM$ . Explaining this with dark matter requires suppressing the dependence on radius, which in turn requires an unnatural fine-tuning between the luminous and dark matter components. It was this that made me start to doubt dark matter before I was cognizant of MOND. When I learned that MOND – and only MOND – predicted this absence of second parameter effects is when I started to take it seriously.

Radial Acceleration Relation

The naive expectation for rotation curves in LCDM follows from placing an exponential disk in an NFW halo. This is the second thing I tried, before the turn of the century, after first trying then-standard pseudo-isothermal halos. This doesn’t work to reproduce the Radial Acceleration Relation (RAR) (or the Mass Discrepancy-Acceleration Relation as I called it back then).

My inability to explain the RAR wasn’t for lack of trying. If it were natural, it would follow naturally, and I would have said so in the ’90s. It did not because the RAR is not natural in terms of dark matter, only in terms of MOND. This used to be obvious to everyone. For example, at a 2006 conference in New Mexico, I said let’s ignore MOND and carefully explained how the data led to what we now call the radial acceleration relation without reference to MOND. As soon as I finished, Anatoly Klypin SHOUTED: “WE DON’T HAVE TO EXPLAIN MOND!”

But we do have to explain the data, which was the whole point of my talk and the paper it was based on (McGaugh 2004). The RAR is in the data, whether you know about MOND or not. Plausible dark matter models could do any number of things that are not that. It’s not my fault that instead the data look like MOND. So, to explain the data, you do have to explain why dark matter looks like MOND (whether you realize it or not), which, as Anatoly correctly grasped, makes no sense whatsoever.

Can a dark matter model be contrived to look like MOND? That was the charge to the galaxy formation community: I wrote McGaugh (2004) to explicitly lay out what we had to do to explain the data conventionally. Nobody took up the challenge. Most of the citations to that paper are MOND-related, it did not draw much response from the intended audience (unless it was a decrease in invitations to speak at conferences like the one in New Mexico). It was old news to me – I had spent several years expanding and vetting the data from the 1998 edition – but I guess it was still too soon to register with most scientists.

The biggest uncertainty in 2004 was the mass-to-light ratios of the stellar populations. I tried a number of prescriptions for these. The RAR was apparent in each; only the best-fit acceleration scale and the amount of scatter varied. So I left that as an “out” – one didn’t have to adopt the same M*/L that MOND fits found (though you need to be close; see above) and wrote the mathematical requirements for the DM halo in all generality. Crickets.

We spent a decade improving the situation with M*/L by acquiring near-IR data. When Federico Lelli first used these to construct the modern RAR, the scatter caused by uncertainty in the previous optical M*/L collapsed to practically nil. The RAR emerged as a tight empirical relation, a result so remarkable that it is in effect a Law of Nature.

This time (2016) the galaxy formation community took notice and fell all over itself to draw the wrong conclusion. Instead of evincing angry denial like Klypin, numerous papers suddenly asserted that the RAR happens “naturally” in LCDM models. If it were so natural, why had the community denied it so hard for so long? This assertion of naturalness is the greatest abuse of scientific language in modern times: there is nothing remotely natural about it; we had already demonstrated this. Those lessons had already been forgotten (if ever learned), but in the intervening time, people had been busily tweaking their models to make them more like data, so if you didn’t know any of the relevant history, or how badly previous models had failed, the assertion that it is all natural might seem reasonable. I guess. It really is not.

In order to build a galaxy formation model, one has to construct a model for both the visible galaxy and its parent DM halo. One of the huge unknowns in this game is how to assign the galaxy we see to a dark matter halo we do not. The standard approach in the 1990s was to assume a constant relation between the mass of the observed galaxy and that of its host dark matter halo. Mo et al. (1998) did this (“the masses of disks are a few percent of those of their haloes”); I made the same assumption in my modeling efforts. It gradually became clear that this could not work, and subsequently abundance matching became the norm for making this assignment. This collapses the dynamic range in halo mass relative to that in galaxy stellar mass, which makes models look like galaxies all live in nearly the same DM halo, which goes in the right direction.

One claim that the RAR is natural in LCDM comes from Navarro et al. (2017). They add exponential disks to NFW halos, duplicating the exercise I tried twenty years earlier. It appears to work better now because they adopt abundance matching to assign DM halos to galaxies rather than the original assumption of a constant ratio of baryons to dark matter that we all made in the hopes of avoiding this becoming a rolling free parameter. The reduced dynamic range in halo mass that follows from abundance matching has the benefit of collapsing models to approximate the RAR, at least over a finite dynamic range. This is illustrated by this plot I made four years ago but I don’t think I’ve published previously:

The radial acceleration relation (top panels) traced by kinematics (red & blue points) and gravitational lensing (orange, cyan, & open points) for early (triangles) and late type (circles) galaxies. Also shown are LCDM models (left) and MOND (right) and their residuals (bottom panels). See text for details.

The data here are kinematic data from our own work plus weak gravitational lensing from Brouwer et al. (2021). Both have been improved since I made this, in particular with the reanalysis of the lensing data by Mistele et al. (2024). Rather than remake the plot, it is informative of how the data improve over time. The lensing data are more reliable where the target galaxies are most likely to be isolated (filled points); less reliable data beyond this region are shown as open points.

Two sets of LCDM models are shown in the left panels. Both have four lines that correspond to the four mass bins used in the weak lensing analysis. The pink lines are the simplest possible: exponential disks in NFW halos. This is identical to the model of Navarro et al. (2017) except that I’ve used Kratsov’s abundance matching relation because this works better for this purpose. The green lines from Li et al. (2022) are similar, but additionally include the effects of adiabatic compression. I omit more complicated models from simulations because the plot becomes incomprehensibly busy. They don’t improve matters.

Over the range $10^{-11} \lesssim \mathrm{g}_{\mathrm{obs}} \lesssim 5 \times 10^{-9}\;\mathrm{m}\,\mathrm{s}^{-2}$ , the LCDM models appear to match the observed RAR. This much supports the claim that LCDM explains the RAR. Is it satisfactory? Is it sufficient?

If one zooms in, as seen in the residuals in the lower panel, the lines for the individual models segregate. This is not obvious in the RAR itself, where the logarithmic scale necessary to display the large dynamic range of the data compresses and conceals such unpleasant details. There is no such mass segregation in the data: all galaxies fall on the same RAR, within the uncertainties.

Another detail that becomes apparent in the residual diagram (which is mysteriously absent in all the papers I’ve seen claiming this works in LCDM) is that the models do not have the right shape. From high to low accelerations, the pink lines dip below the data, then above, then below again. At low accelerations, they dive very much below: the models cease to even come close to working at $\mathrm{g}_{\mathrm{obs}} \lesssim 10^{-11}\;\mathrm{m}\,\mathrm{s}^{-2}$ . Their utility is limited to a narrow dynamic range: they are neither satisfactory nor sufficient.

The models considered here do not probe the high acceleration end of the RAR. This is an artifact of the simplicity of the exponential disk plus NFW halo model. Such models never reach high accelerations because those are the province of bulge components. Without those, the models end in little hooks: they are turning away from the RAR at the highest acceleration plotted. There’s no reason not to plot to higher acceleration, but it would make the models look worse – the hooks would grow in the wrong direction. I’ve made the conscious choice – as I’ve noted others have – not to show the ugly parts of this model. The difference is that I don’t pretend it works by virtue of not looking where it doesn’t work.

The models from Li et al. (2022) that include adiabatic compression are represented by the green lines. These do better than the simple exponential disk plus NFW halo models insofar as the are less bendy. But they still segregate by mass, and dive to lower accelerations even faster.

I’ve tried various simulations in this plot but I have yet to find one that does well. The turn down at low accelerations occurs at large radii where feedback effects are usually said to be minimal, so that is not a likely solution. Indeed, the problem is generic. Low accelerations probe the outer regions of CDM halos where the robust prediction from simulations is a density profile that scales as $\rho_{\mathrm{CDM}} \propto r^{-3}$ , but the data scale as $\rho_{\mathrm{DM}} \propto r^{-2}$ as required to produce a flat rotation curve. Consequently, the mismatch between CDM and the RAR at low acceleration is serious.

In contrast, MOND does fine. It explains the data at all observed acceleration scales, not just a narrow window. The agreement now is better than is depicted with these older data, but this is already good. The only objection one might raise is that the lowest accelerations obtained from gravitational lensing for early type galaxies are offset from the prediction of MOND. (The open triangles sit above the zero residual line in the lower right panel.) This is largely rectified in subsequent analysis, as an experienced astronomer might expect, but this didn’t prevent people from leaping at this mild discrepancy as evidence against MOND. It would be, if it were true. It would also be bad news for LCDM, as these same data are even more discrepant from the models at left. This is a good example of the bias that infects the field: any discrepancy from MOND is seen as a win for dark matter – even when dark matter suffers the same problem (or worse).

Central Surface Density Relation

In MOND, the observed mass determines the kinematics through the modified Poisson equation. Just as lower accelerations mean larger mass discrepancies, so too do lower surface densities mean lower accelerations. Consequently, one expects a relation between the characteristic surface density of a galaxy and the amplitude of the mass discrepancy it evinces. In ignorance of that, Erwin de Blok and I discovered that low surface brightness galaxies were dark matter dominated. It wasn’t just “gee, there’s a lot of dark matter here;” the amplitude of the discrepancy correlates with central surface brightness.

This can be quantified by the central surface density relation:

**Fig. 2** from Lelli et al (2016). *The central* dynamical *mass surface density as a function of the central* stellar surface density (left) and stellar mass (right). Points are color coded by morphological type. The dashed line shows the 1:1 relation expected in the absence of dark matter; a fit to the data (dotted line) is consistent with the prediction of MOND.

This relation involves the central regions of galaxies. High surface brightness galaxies are far enough in the Newtonian regime ( $G \Sigma_{\star} \gtrsim a_0$ ) that they follow the one-to-one line: what you see is what you get. Lower surface brightness galaxies diverge from the one-to-one line, having systematically lower accelerations ( $G \Sigma_{\star} < a_0$ ) and larger mass discrepancies (i.e., they appear to need more dark matter) as surface brightness decreases. There is no reason for this behavior in dark matter, for which the central surface density of stars is not a parameter of obvious relevance.

The central surface density relation is both natural and expected in MOND. I am not aware of a dark matter model that addresses this relation. The correlation with mass (right panel above) is often discussed, and is considered to be deeply meaningful by some. However, the correlation in the right panel occurs entirely because stellar mass correlates with surface brightness, albeit imperfectly, so the right panel is a blurry version of the left panel. The surface density of stars is the important parameter here, not their total mass.

Renzo’s rule

There are other ways to see the connection between kinematics and the distribution of observed baryons. Indeed, a connection was recognized empirically by one of the great 21 cm observers, Renzo Sancisi. To quote from his abstract from IAU 220:

In the inner parts of spiral galaxies, of high or low surface brightness, there is a close correlation between rotation curve shape and light distribution. For any feature in the luminosity profile there is a corresponding feature in the rotation curve and vice versa. This implies that the gravitational potential is strongly correlated with the distribution of luminosity: either the luminous mass dominates or there is a close coupling between luminous and dark matter.

Sancisi (2003)

The shape of the rotation curve correlates with the shape predicted by Newton for the baryons:

Two galaxies exemplifying Renzo’s rule. Images of both galaxies are shown together with their rotation curves (open points), Newtonian rotation curves for the observed stars and gas (gray lines), and the corresponding MOND rotation curves (blue lines). In the high surface brightness spiral NGC 6946, the compact central bulge component predicts a sharp inner bump in the rotation curve that declines before it rises again. In the gas-rich dwarf NGC 1560, there is a broad feature in the gas that is reflected in the rotation curve. (Adapted from Fig. 21 of Famaey & McGaugh 2012; images added.)

This phenomenology is common enough for Prof. Sancisi to notice through the experience of looking at lots of data. Indeed, he said it to me in person in 1995 when we had a heated debate about the interpretation of the Tully-Fisher relation. The correspondence he noted implies that baryons are important to the mass budget, in both high and low surface brightness galaxies. In contrast, the absence of surface brightness-dependent residuals in the Tully-Fisher relation implied that LSB galaxies were certainly sub-maximal, and HSB galaxies as well if one desires to avoid fine-tuning.

Our discussion was heated in the best way. We weren’t angry, just engaged. We understood both things could not be true, but apparently they were. I redoubled my efforts to look for residuals from Tully-Fisher, ultimately finding none after many years of checking. Renzo held off on publishing his statement (for eight years!) while he looked at more LSB galaxies. Both results were sustained at the level expected for astronomical data despite the contradiction they encapsulate.

The correspondence of features (sometimes referred to as “bumps and wiggles”) in galaxy luminosity profiles and rotation curves makes sense in HSB galaxies if they are maximal in the sense discussed above. If instead dark matter dominates, there is no reason for the rotation curve to reflect the features in the baryons. Indeed, it cannot: the observed bumps and wiggles are typically features like spiral arms that require disk self-gravity to support them. The dynamics of quasi-spherical dark matter halos simply can’t support features like that – the phase space of particle orbits is too different. Even if they could, which they can’t, there would be no reason for the correspondence: the DM halo might have its own features, which if its mass dominates, could be anywhere, not where we see features in the stars.

This issue becomes more pronounced in LSB galaxies. Since the mass discrepancy is large at all radii in LSB galaxies, the mass of the DM halo always dominates. There should never be a correspondence of features, and yet there are.

The only theory that satisfactorily explains both the correspondence of features in Renzo’s rule and the absence of surface brightness-dependent residuals from Tully-Fisher is MOND.

The acceleration scale

Threading throughout the data is the acceleration scale $a_0 = 1.2 \times 10^{-10}\;\mathrm{m}\,\mathrm{s}^{-2}$ suggested by Milgrom. This shows up in the data in many ways. Three of these are summarized in this plot from the review by Lelli (2022):

The BTFR shows that all galaxies share the acceleration scale $a_{\mathrm{BTFR}} = {V_f^4}/{(GM)}$ . The acceleration scale $a_{\mathrm{RAR}}$ is where the RAR bends away from Newtonian behavior. Similarly, the surface density of the bend in the central surface density relation, $\Sigma_{\mathrm{CSDR}}$ , marks the acceleration $a_{\mathrm{CSDR}} = 2 \pi G \Sigma_{\mathrm{CSDR}}$ . These relations need not exist at all in a universe dominated by dark matter. Even if they do for some reason, there is no reason to expect they all share the same acceleration scale. Yet within the uncertainties, they do: $a_{\mathrm{BTFR}} = a_{\mathrm{RAR}} = a_{\mathrm{CSDR}} = a_0$ .

Cold dark matter is scale free, so an acceleration scale is not natural to it. That doesn’t prevent people from asserting it is. Kaplinghat & Turner (2002) do just that. The absurdity^$ of this claim was immediately pointed out by Milgrom (2002), but this has not precluded either Kaplinghat or Turner from continuing to assert that they’ve explained that which they have not remotely explained. It’s more like a political talking point than science.

Exceptions

The table above lists some of the rules that the vast majority of galaxies obey. I emphasize vast majority because relations like Tully-Fisher would be unrecognizable if there were lots of exceptions. It wouldn’t be a relation at all. We need to understand the rules the majority obey – which we do not in the context of dark matter – before obsessing about potential exceptions. To do the latter is a classic case of missing the forest for the trees.

There are always exceptions in astronomy. These come in several flavors: (i) goofs, (ii) apparent exceptions that actually prove the rule, and (iii) genuine exceptions that falsify a theory (anomalies). The first category is extraordinarily common in astronomy, the second can take a long time to recognize, and the third are rare if they exist at all. New examples in each category are always being discovered, so it is a Sisyphean task to check every case.

The most common flavor of exception in astronomy is the straight-up goof (i). These are so common, the experienced astronomer is rightly skeptical of a story that lacks exceptions. In the case of MOND, there have been many galaxies that appear to be problematic but later turn out not to be. They’re just goofs. There have been so many examples of this, I have lost count. Over a hundred, easily.

The ultra-faint dwarf galaxy Boötes III provides a recent example of an ordinary goof. Ultrafaint dwarfs often have velocity dispersions well in excess of that predicted by MOND, but it is challenging to measure dispersions as low as predicted. In this case, Ting et al. (2026) “measure a velocity dispersion of σ_v = 1.69 +1.03/−0.85 km s⁻¹, about six times smaller than the previously reported 10.7±3.5 km s⁻¹.” The larger number has been known for a while and is strongly inconsistent with MOND; the new measurement is pretty much bang on what MOND predicts. Consequently, one can see how it is easy to leap to the wrong conclusion, especially with confirmation bias standing behind you ready to push as you look out over the cliff.

Apparent exceptions (ii) are outliers that appear to violate a rule, and do so with high significance. In these cases, it is the rule that is not always universal. Relations like the BTFR and RAR are predicted by MOND and hold for the vast majority of galaxies. There are, however, some genuine outliers.

One can imagine building a DM model that reproduces these things. (I’m not even requiring it to be satisfactory for the moment.) Then, when one encounters an object that falls off these relations, you might conclude MOND is wrong and the DM model is better because DM tolerates outliers better (often by virtue of having no good reason for the relation in the first place). Some objects happen not to follow the statistical happenstance of the DM model, while you can’t turn off the force-law in MOND, so the rule must always apply. Right?

The problem with this reasoning is that MOND does predict exceptions. Objects for which the external field is important should deviate from the main relation that holds for isolated galaxies. I have seen many cases where what looks like a failure of MOND is actually a corroboration once you consider the external field. Such cases are a problem for our hypothetical DM model: once we construct something up that explains a relation like the BTFR, outliers can happen, but should not depend on the acceleration of from an external field. The external acceleration from some external source simply has no role to play in dark matter models.

Finally, there are genuine anomalies (iii) that would indeed falsify MOND. Most examples that I have seen that seemed to be in this category have later turned out to be in one of the first two categories: simple goofs or predicted exceptions. Some cases are still under litigation, and new examples will be discovered in the future. Do I know that all these will all work out? No, of course not. Have I seen this movie enough times to have a well-founded empirical expectation that they probably will? Yes, I have.

Dark Matter as extra, invisible mass is practically falsified

Look at the table above again. Time after time after time, new observations have been made that were not predicted by dark matter but were by MOND. Dark matter simply does not succeed in predicting galaxy dynamics the way MOND does. That’s very telling.

Many scientists choose to ignore MOND’s predictive success, or have sought to downplay its importance. When they bother to do the latter, they usually restrict themselves to a single item, often in apparent ignorance of the rest of the table. For example, a common talking point is “MOND only fits rotation curves!” Never mind that “only” here is a falsehood. The “mere” ability to fit rotation curves is already a highly non-trivial result. Each and every galaxy has its own unique mass distribution and poses a separate test of MOND, just as every planet and every comet and every asteroid test Newton’s law of gravity in the solar system. We’ve made hundreds of these tests: the effective force law in galaxies is MOND.

More generally, it isn’t just that the relations listed in the table above were correctly predicted by MOND and not by dark matter. It is also that the post hoc dark matter explanations are not satisfactory. Sometimes they are mutually contradictory.

The only way to save dark matter is to contrive for it to look like MOND. It is hard to think of a more damning statement about an otherwise nebulous hypothesis. Dark matter could be anything, do anything, and yet the one thing it has to do is mimic the very precise and comparatively inflexible predictions of its chief rival.

The needle in the dark matter haystack. Galaxies might lie anywhere in this voluminous, multiparameter space, but in practice they inevitably seem to reside in the negligibly small part of the volume that “looks like” MOND.

Can a dark matter model be contrived to look like MOND? Many have claimed to do this, even asserted that it happens “naturally.” This latter assertion is the greatest abuse of scientific language in modern times: there is nothing remotely natural about it. If it were natural, it would follow naturally, and I would have found that and said so in the ’90s. A corollary is that the people who claim now to explain it naturally would not have spent the intervening decades loudly denying that it could be so before they suddenly knew it all along. Lord knows I’ve tried to build acceptable DM models, and there are always more (increasingly silly) things to try, so when I say that I do not think it can be done, at least not with conventional flavors of DM, it is a highly nontrivial statement^.

When the dark matter paradigm took off, we had lots of indications of mass discrepancies. Flat rotation curves required more mass than they eye could see; the gravitating cosmic mass density exceeded that attributable to baryons. The vast majority of dark matter candidates currently being contemplated are informed by that perspective. As such, they simply come up with a new particle that could provide the extra mass.

That approach was sufficient in the 1980s, but since then new shit has come to light.

Many items in the table above constitute new stuff that has come to light since the DM paradigm was established. It isn’t just that rotation curves are flat and therefore we need more mass. It is also that the amplitude of the flat rotation speed correlates with the baryonic mass (the BTFR). And that the kinematic acceleration correlates with that predicted by Newton for the observed distribution of baryons (the RAR). And the rest of the table. New shit has come to light! These things did not inform the development of the dark matter paradigm, and are not explained merely by invoking invisible mass. We need to reexamine the paradigm in that new light.

The BTFR and the RAR and the other observations detailed above all point to a strong connection between baryons and dark matter, completely the opposite of the original mandate. Extra, non-interacting, invisible mass might still suffice for cosmology, but explaining galaxy dynamics is more demanding. Just adding invisible mass does not explain the strong coupling with the observed distribution of ordinary baryons. A viable dark matter candidate needs to do this, but the vast majority of them have been constructed in ignorance (or denial) of the need to explain the MONDian phenomenology.

I can imagine a non-generic DM candidate might be engineered to satisfy all needs. There are candidates that attempt to do this, like dipolar dark matter or superfluid dark matter. This post is long enough, so I won’t say more about those here. What I am convinced will not work is relying on feedback to somehow change the essence of CDM to mimic MOND. That’s a pipe dream akin to profiting from stealing underwear.

*? = feedback? (Underwear gnomes from South Park.)*

The observed kinematics of galaxies as described above suffice by themselves to provide a practical falsification of dark matter as widely conceived – either CMD specifically or generic extra-mass DM, excepting only highly specific ideas that build-in MOND-like behavior. (I say a practical falsification because outright falsification is impossible with unseen entities.) There are other, independent reasons to doubt DM, like the apparent absence of the expected dynamical friction due to dark matter. There are of course reasons to persist with DM, but it needs to be more than some random particle that just adds mass to the universe.

It is not possible to make progress in the context of dark matter without addressing the observed phenomenology described above as a whole rather than the common, piecemeal, divide-and-deny approach. We will not consider alternative theories until we agree that dark matter, as currently conceived, is wrong. We are stuck in a rut, and have been for a long time.

*It also shows the rotation curve that would be measured from the gas, which differs from the actual rotation curve in many simulations. This seems to have led many simulators to disbelieve observed rotation curves, but this is a simulation problem not an observational problem. We know how to recognize and correct for non-circular motions in the data. These corrections are usually small and the data never look like these simulations. It’d be really obvious in the velocity fields of real galaxies were messed up in this way. (Real galaxies are often messed up, just not in the ways seen in LCDM simulations.)

^#There can also be nuisance parameters like distance and inclination. These are measured independently and ideally would be held fixed, but of course there are uncertainties on these values so one can marginalize over the range of allowed possibilities. The same is true in DM halo fits.

^$Milgrom’s rebuttal is quite thorough, so I don’t want to pile on. But the acceleration scale appears in diagrams like the RAR that plot an observed kinematic acceleration ( $\mathrm{g}_{\mathrm{obs}}$ ) against one obtained from the observed baryons ( $\mathrm{g}_{\mathrm{bar}}$ ). In terms of dark matter, $\mathrm{g}_{\mathrm{obs}} = \mathrm{g}_{\mathrm{bar}} + \mathrm{g}_{\mathrm{DM}}$ . K&T talk about the dark matter; but have no model for the baryons, which are essential to both axes of the RAR. They make a hand waving argument that $a_0$ corresponds to the edge of galactic disks, which it does not – that’s what low surface brightness galaxies had already taught us by then. So they don’t explain the acceleration scale at all.

^I’m sure galaxy formation theorists can be found who will sanguinely assure us that all that needs to be done can be done, it’s just a matter of tweaking this or that. So why haven’t they succeeded in thirty years of effort? So far, they’ve mostly just come up with more elaborate versions of models I already tried and rejected as obviously unworkable. Making them more elaborate doesn’t make them less wrong.

What can’t it be?

I’ve been trying to think more seriously about the entity that set off the LZ experiment. I was dismissive of the possibility of it being dark matter, perhaps unfairly so. On further reflection, I feel only fairly dismissive.

First, the formal significance that is claimed is 2.6σ. That seems to be a fair and fairly conservative statement. So it seems something did happen, the question is what. The odds of a 2.6σ event are about 1 in 200, so a fluke seems unlikely.

I can think of three generic possibilities:

It’s a fluke.
It’s dark matter (huzzah!)
It’s some strange new particle-entity that is not dark matter.

I remain of the opinion that the most likely possibility is that is is a fluke. I know I just said that seems unlikely, but “seems” is doing a lot of work here. I think it is fair to say that known explanations are excluded at this confidence, but that leaves a lot of unknowns. Most unknowns turn out to be boring.

We’ve been down this road many times. The LHC has been running for many years now. It detected the Higgs particle, which was the last missing piece of the Standard Model. That’s a great success. It was hoped that the LHC would also reveal new physics beyond the Standard Model. That it has not done. But there have been many hints during its operation. These appear as glitches (deviations from expectation); there have been multiple glitches that appeared to be significant at the 2.something σ level. Each time such a glitch was reported, it resulted in a flurry of theoretical activity. Within days, the arxiv preprint server would be inundated with hundreds (literally hundreds) of preprints staking out a claim as to what the latest glitch might be. Each time more data were acquired, the glitch went away. So this seems like another such occasion, making (1), a fluke, seem like the least improbable outcome.

This is why the [arbitrary] threshold for discovery is set at 5σ (1 in 3.5 million). Flukes at the 2.something σ level happen too easily, too often. This phenomenon is not restricted to particle physics. The same thing happens in astronomy all the time. All the gorram time. It’s almost as if nature places more probability in the tail of the distribution for “weird” events than the Gaussian statistics we use say there should be.

Given this experience, finding a new particle outside the bounds of the Standard Model of Particle Physics seems a lot less likely than 1 in 200. Seems is again doing a lot of work here. How likely 1 in 200 hundred seems depends on your priors. If you’ve been working on this for a long time in the hopes of a positive result, these odds seem pretty good:

“I have been waiting for a positive result for, oh, my god, 40 years. So you can bet I’m very, very excited by the LZ results.”

Katy Freese

If, like me, you’ve already convinced yourself that dark matter cannot explain the kinematic data for galaxies, then it is just another opportunity for the eyes to roll up inside the skull. Obviously we can’t both be right, which is why we do these experiments.

So what about the other possibilities, (2) and (3)? If the event is real, it is tempting to believe that it is dark matter. That’s what the experiment was designed to detect, after all, so that’s a natural first assumption. But just because you’re looking for something doesn’t guarantee that when you find something you find what you’ve been looking for.

As I’ve reviewed before, we’re way past the regime of what we expected to find. So it’d be great to find something, but there’s little reason at this point to expect that something to be what we set out to find. So it might be dark matter (2) or it might be something completely different (3). I’ve no way to weigh the odds of those possibilities because they both seem very unlikely.

For WIMP-like dark matter we at least have some expectations, and this event does not conform to those expectations. It is too high energy. For every event like this one, the detector should have already recorded lots and lots of lower energy events.

That doesn’t mean it isn’t dark matter (2), just that it isn’t what we expected. But we already missed out on what we were expecting, so maybe? Or maybe it is something unrelated (3), or nothing at all (1). One event does not help override whatever assumption bias we might have had about these possibilities to start.

To be convincing…

It occurs to me that I am likely to hold the putative detection of dark matter to a higher standard than other scientists. So what would I find convincing?

First, the detection of a putative new particle has to cross the traditional 5σ threshold.
Second, the same result must be obtained by independent experiments.
Third, the new particle has to be demonstrated to have the right properties to be dark matter.
Fourth, the new particle has to exist with the required mass density to be the dark matter.
(Fifth, it should naturally explain the observed MONDian phenomenology.)

I put the fifth criterion in parentheses because it is a very high bar, and I can conceive of being persuaded to soften it. It is also more advanced tuition than most physicists have contemplated, so let’s start with the more basic requirements.

At present, none of the above criteria have been met by the new LZ result. There is an old claim to a significant detection by DAMA that satisfies the first criterion but was never independently reproduced, so fails the second criterion. Nobody outside the original experiment takes it seriously now for that reason. It is sobering to realize that while new and exciting, LZ has not yet progressed as far down this list as DAMA.

Supposing both the first and second requirements are met, then we have a new particle. That is certainly interesting, but by itself would not mean we’ve found dark matter. When we’re in the realm of imagining new particles, there is a vast landscape of possibilities. Only some features in that landscape could qualify as dark matter; there are other possibilities that could exist but have nothing whatever to do with dark matter. So the properties of the particle have to be right, and there is a long list to satisfy.

From a generic astronomical perspective, the fourth criterion is the most important. We have a pretty good idea of the mass density that dark matter needs to have in the solar neighborhood to explain Galactic kinematics. That’s what these experiments are trying to detect: the dark matter particles in our Galaxy’s dark matter halo that happen to be passing through just now. So for whatever we detect to qualify as the dark matter, there needs to be the right number of particles with the right mass to satisfy astronomical requirements.

This fourth criterion is a pretty high bar. It does not suffice merely to find a new particle, it’s gotta be the right kind of particle and these particles have to exist with the right density. That can be measured, but it requires lots of detections: enough to work out the properties of the particles and how many are whizzing by. This is part of the disconnect I had in the last post with people complaining about statistical significance: they were focused on the significance of this one event; I was worried about having enough detections to estimate the mass density, or at least see if it is anywhere near the right ballpark. I’m more concerned with the astrophysical relevance of a new particle than with the new particle itself.

This is a generic problem in the field of dark matter, being as it is at the interface of two different fields. Astronomers need dark matter; we don’t care so much what it is if it performs as required. Particle physicists heard we astronomers needed dark matter, so are more than happy to suggest possibilities, but are more interested in the particle itself than what it does for galaxies. I don’t say what it does for the universe because that’s a lower bar where any dynamically cold, non-baryonic mass will do. The cosmic density needs to be right, but there’s no way to measure the cosmic average, only the local density of the Galactic dark matter halo.

The highest bar is the fifth criterion, which I think warrants its own post.

Yep, it’s a religion

I have been concerned for years that dark matter was morphing from legitimate science into a cold, dark religion. I have been reluctant to put it that way, because there are lots of scientists who work on dark matter that have not fallen entirely down that rabbit hole and who continue to make valuable contributions working in that context. But a recent experience reminded me that my concerns were not misplaced, and there are plenty of scientists who have fallen irredeemably down this rabbit hole. No matter what answer the future holds to be correct, many current scientists will have gone to their graves in denial of it.

Where is the boundary between science and religion? It is hard to assess where the borderline is. But it is easy to see when people are far over the line – so far over that it doesn’t really matter where exactly the line is. One can attend any conference on the subject to find people who unabashedly assert that dark matter exists without question. Not just that acceleration discrepancies have been amply demonstrated empirically, but that the only possible interpretation is dark matter. If asked whether this invisible mass is in the room with us now, they will enthusiastically^# answer yes! Since dark matter has not been detected in the laboratory, this assertion is an expression of faith – the hallmark of religion – not of an established scientific fact. What we have established is that there are discrepancies between what we see and what we get when we assume Newtonian gravity (or GR, if needed). What we don’t know is whether the cause of these discrepancies is some form of invisible mass (dark matter) or if the equations we employ are inadequate (modified gravity [or more generally, dynamics]).

Indeed, these days many people will assert that dark matter has already been detected, usually citing astronomical evidence that used to be considered too feeble to merit a Nobel prize. Funny how repeating a mantra long enough morphs an aspiration into accepted reality. Modern physics is not providing a strong falsification of the supposition that science is a social construct.

A prominent example of an observation of the sky that is frequently cited as absolutely requiring cold dark matter is the acoustic power spectrum of the cosmic microwave background. Quoting clayton from a few years ago:

the primary reason to believe in the phenomenon of cold dark matter is the very high precision with which we measure the CMB power spectrum, especially modes beyond the second acoustic peak. There is a stone-cold, qualitative, crystal clear prediction of CDM about the relative sizes of the second and third peaks that modified gravity profoundly and irredeemably gets wrong: it thinks the third peak should be relatively larger* than the second… whereas CDM thinks they should be about the same

I would accept that this were conclusive proof of dark matter if this were the unique prediction of dark matter: that there was no other way to do it, so all other approaches were indeed irredeemable. (Quite the strong language, eh?) The problem is that CDM is not the one unique was to fit these data. Skordis & Zlosnik showed that it is possible to write a modified gravity theory that also fits the CMB data:

*CMB power spectrum observed by Planck fit by AeST (Skordis & Zlosnik 2021).*

This does not prove the AeST theory of Skordis & Zlosnik is correct, but it does demonstrate that it is possible to write a modified gravity theory that does indeed do what it is frequently asserted to be impossible for a modified gravity theory to do. I’ve heard of a couple of other theories that can also do this (the relativistic Khronon theory of Blanchet and nonlocal MOND as discussed by Deffayet & Woodard), so clearly this success is not uniquely limited to cold dark matter, or even a particular modified gravity theory. The work of Skordis & Zlosnik (2021) was known and in the literature before clayton made the assertion above in late 2022, so either he wasn’t paying attention (likely) or is convinced that it is impossible so doesn’t even consider the possibility (also likely). The former just says we’re all too busy, but the latter is a mark of religious thinking: my god is the only god, thou shalt have no other hypotheses before^& me.

Many people are very impressed with the quality of the LCDM fit to the CMB. That is indeed very good, but there are enough free parameters that we were going to get a fit to any physically plausible power spectrum. If not, we’ve never been shy about making up new parameters. (Evolving dark energy, anyone? How about a running power spectrum? There’s a whole bag of possibilities!) What I’ve been more impressed with is the consistency of the fit to the CMB data with the many independent constraints on conventional cosmology. Or at least it was, until it wasn’t.

The Hubble tension has gotten steadily worse (in terms of statistical significance), and it really does not look like local measurements are to blame, nor is it the only tension. People seem to miss that it is the CMB-fitted value of the Hubble constant that has evolved over time to spoil the concordance that got us to believe in LCDM in the first place. But if the CMB is the cornerstone of your religion, all other data must inevitably be at fault and can be ignored: there is an entire community of cosmologists who choose to believe the best-fit Planck cosmology to the exclusion of all other data. It’s like the bad old days of the Hubble tension all over again, with the physics community choosing to believe the lower value of H₀ because it makes more sense for the aspects of cosmology that they care about while those in the astronomical community who actually measure H₀ find a persistently higher value.

A real tension in LCDM implies the need for new physics of the unknown variety. One doesn’t want to go there if it can be helped. I didn’t consider MOND until I was already concerned for the viability of dark matter. There are real problems for the paradigm that its more intense advocates simply deny, brush aside without real thought, or choose to remain ignorant of. When they are confronted with a problem, they are pretty creative about making stuff up on the spot. Anything to avoid having to confront the unspeakable – another hallmark of religion.

For example, cold dark matter is scale free. That’s foundational to the hypothesis. So the existence of an acceleration scale in the kinematic data is anathema to CDM. When I first pointed this contradiction out, there were a variety of assertions to the effect of “does too!” One example is provided by Kaplinghat & Turner, who claim to show “how Milgrom’s law comes about in the cold dark matter theory of structure formation.” That would, indeed, be ideal, and is a requirement for any theory to be successful.

Wee problem: they demonstrat no such thing. CDM is scale free, yet K&T claim that it explains Milgrom’s Law, which is predicated on the existence of an acceleration scale. Well, which is it? Is CDM scale free? Or does it explains the acceleration scale? We can’t have it both ways: their very premise is self-contradictory. It is absurd on its face.

The acceleration scale is defined by baryons, for which K&T have no model. To connect baryons with dark matter, they make a hand-waving argument about galaxies reaching a₀ at the edge of their disks. This is not even a concept of a model and does not begin to suffice as an explanation for many reasons, a prominent one being that low surface brightness galaxies have accelerations less than a₀ everywhere:

Centripetal acceleration curves color coded by galaxy surface brightness. Low surface brightness galaxies (blue colors) have low (sub-a₀) accelerations everywhere: there is no edge at which they reach a₀. (Adapted from McGaugh 2020.)

Milgrom pointed out this and many other shortcomings of their scenario, so I feel no need to elaborate further. Milgrom eviscerated their paper so thoroughly that the proper course of action would have been to retract it. Instead, they simply never acknowledge the criticism, and persist to this day in pushing it as some sort of valid scientific explanation. It is not; it does not withstand even mild critical scrutiny. But it doesn’t need to: it reassures the faithful that all is well. They hear what they want to hear without questioning its veracity. That’s another hallmark of religion.

I have refrained from saying these things in the past because I’m too nice. For example, a few years ago I started then abandoned the draft text below, which I simply cut & paste:

One of the things that attracted me to a career in science is the notion of objectivity. I grew up for a time in the bible belt, where people earnestly believed things that were obviously untrue, even to the eyes of a small child. On the occasions that I had the temerity to point out the obvious, the contradictions posed by facts never had an impact on their belief system. Rather, it inevitably earned me a warning that I was going to hell. No few of these people seemed to think it was their religious duty to send me there prematurely, or at least to make life on Earth a living hell.

Scientists eschew such behavior, but are also human, so often engage in it anyway. I’ve encountered it a lot. I get it; I went through the same denial, grief, and anger over the prospect of losing my good friend cold dark matter. The stages of grief never brought something back from the dead, but it has engendered a lot of blame-the-messenger.

Here’s an example, from a review by Mike Turner:

There is a lot of misinformation packed into this short paragraph.

The first clue is right there at the beginning, in red: the heading “False starts.” This is false framing, a classic tool of propagandists. It starts from the outset by asserting that the topic to be discussed is wrong at a level of knowledge so common it requires no justification. This is not the way one starts an objective discussion, much less a scientific one.

Turner then misconstrues what Milgrom did. He didn’t notice the scale a₀ in the data, for which there was scant evidence at the time. Rather, Milgrom made the obvious statement that the inference of dark matter relied on the assumption that dynamics, as encapsulated by the laws of inertia and gravity, is the same on the very different scales of galaxies as in the solar system where they were established, so we ought to consider if dynamics might change in some way. He quickly excluded a size dependence as a possibility. How he settled on acceleration is beyond the scope of this post, and not for me to say. Neither is it for Turner to say.

After a brief and incomplete description of what MOND is, Turner allows that “this one-parameter model fits all the rotation-curve data”. Even in making this admission, he chooses to call it a model rather than a theory. A model is something specific you build in the context of a theory, like a halo model in CDM. MOND is more than that.

Turner quickly moves on without contemplating any meaning that rotation curves might hold. Let’s pause to consider that.

First, I would not say that MOND fits all the rotation curve data. It fits most galaxies, but there are a minority of weird cases that are not well fit. The weird cases inevitably don’t make sense in terms of dark matter either, so on the whole I interpret this to be the usual price of dealing with astronomical data – some of it is just goofy. Setting such cases aside, I can and have fit the same data with all sorts of dark matter halo models. MOND requires fewer parameters, which is important, but the difference isn’t in the fitting. The difference is in predictive ability. I can use MOND to predict the dynamics of galaxies a priori, and have done so many times. I cannot use any flavor of dark matter theory to do the same, and it’s not for lack of trying.

The predictive power of MOND must be telling us something, even if it is something about the nature of dark matter or the process of galaxy formation. There are many papers written on this, some deep and profound, others absurd and banal. Turner cites none of them, nor displays any awareness that such work exists. I would venture to guess that is because acknowledging such work would imply that there is something to debate here, something he would apparently rather not admit.

That’s where I left off. It’s exhausting deciphering other people’s false assertions. Moreover, I just don’t like criticizing other people, no matter how richly they deserve it. (Turner has never refrained from criticizing me in ad hominem terms: on one occasion^$ he showed my picture to an audience and called me “the enemy.”) A large segment of the particle physics and cosmology community appears to think this way, and has succumbed to a scientific version of bible thumping in which you can assert any absurd thing so long as it falls within the framework of the holy LCDM. They really need to find something better to do.

I had hoped we were past this, but I heard a talk last week that was exactly in this mode. To paraphrase, the talk went

We’re sure dark matter exists. We have been sure about it for decades. In that time, we have been repeatedly proven wrong about what it is. Rather than re-think our paradigm in the face of these repeated failures, we double down yet again on the existence of this invisible, undetected mass, asserting aggressively^% that it must be true while eliding or misrepresenting the evidence that it is not. This enables us to make up a whole lot of exciting new possibilities for what the dark matter might be and conceive of ever more grandiose experiments to continue not to detect it. You must believe in dark matter!

This was not a science talk so much as an indoctrination session. It was as if I had stumbled into a revivalist tent where some hothead was preaching to the choir. This is the kind of talk that misled an entire generation into wasting their careers at the bottom of a mine shaft searching for WIMPs. At least WIMPs were a well-motivated hypothesis; this kind of talk could lead a new generation down an even greater variety of garden paths.

I am well aware that I might fall prey to this attitude myself. That’s why I set criteria by which I would change my mind: detect dark matter already, or at least provide a satisfactory explanation as to how MOND comes about. Neither of those criteria have been met. There are claims to do the latter, but so far these are just variations on models I tried and found to fail long ago. If I thought these could work, I would have said so. At the same time, I don’t see any dark matter advocates taking up the challenge to specify what would change their minds. When I ask them what could falsify dark matter, I get dumbfounded looks – the deer-in-the-headlight face one gets when the immediate response why would you even ask that? is checked by a distant memory that scientific theories are supposed to be falsifiable.

Personally, I found it humbling to encounter MOND in my own data. I too thought we understood the universe with dark matter. But who ordered this? Certainly not me: my own conventional, dark-matter based predictions were falsified. No one else working in the context of dark matter had got it right at the time either. Only Milgrom ordered this.

And what is this? There is a direct connection between what we see and what we get. Even in ignorance of MOND, the radial acceleration relation encodes a one-to-one relation between the distribution of baryons and the effective force. This is so direct that one can right down a single equation connecting the two:

g_{obs} = F(g_N/a_0)\,g_N.

The observed acceleration is a simple function of that predicted by Newton for the stars and gas that we see. There is no mention of unseen mass; everything is specified by what we can see is there.

I’ve sometimes heard astronomers complain about the reductionist ethos of physics, trying to cram all the complexity of the entire universe into a theory of everything. But here it is appropriate: there is a single, apparently universal force-law at work in galaxies. That’s telling us something profound. And yet if questioned about this, the physicists are the ones who will complain that galaxies are complicated, so they should be exempted from having to explain them. Galaxies should be complicated – in LCDM. But they’re observed not to be, in the sense that a single equation suffices to describe their kinematics. The problem isn’t that galaxies are inexplicably complicated, it’s that they should be but aren’t.

I am deeply disappointed that many scientists apparently lack the physical intuition to immediately recognize the import of the simple relation between what we see and what we get. It is the same sort of thing Newton noticed in the solar system: everything happens as if the gravitational force is proportional to the product of the masses and the inverse square of their separation. He didn’t understand why at the time, and was criticized for indulging in magical thinking: how can there be action at a distance? But that’s what the data were saying, and the same applies now. We might not yet understand the why, but that the data look as if MOND is what’s happening in this universe.

^#The framing has morphed over the years. A recent advent is that some people have started proactively asserting that invisible mass is in the room with us now in order to avoid having to answer it as a question that makes them sound like loonies.

*He means the third peak should be smaller than the second, not larger, if by “it” he means modified gravity with the baryon density expected from big bang nucleosynthesis, which was the hypothesis that correctly predicted the first-to-second peak ratio but does indeed get the second-to-third peak ratio wrong. Funny how the CMB community was able to completely ignore the successful prediction for several years, but were then suddenly all over the latter failure. The third peak falsifies the ansatz on which that particular prediction was built, not the entire concept of modified gravity. This would be like asserting that all possible forms of dark matter are excluded because we haven’t yet detected WIMPs. It is a classic failure of objectivity, which is another hallmark of faith-based argumentation: we know His name is [insert favorite deity], not [insert any other deity].

^&Or after me. Dark matter was my first hypothesis, and I’m here to tell you that True Believers do not suffer second hypotheses or those who stray from the fold. I guess that’s why so many scientists who are MOND-curious keep it on the down low. Wise, perhaps (that’s why tenure needs to be a thing), but hardly the ideal of the open and free exchange of scientific ideas.

^$I wasn’t there, but one audience member (not someone I knew) thought it was so over the top that he told me about it, sharing a link with a video. (I did not retain that link, and doubt the hosting conference website is still active.)

^%Argument weak here. RAISE VOICE!

Has dark matter been detected in the Milky Way?

If a title is posed as a question, the answer is usually

No.

There has been a little bit of noise that dark matter might have been detected near the center of the Milky Way. The chatter seems to have died down quickly, for, as usual, this claim is greatly exaggerated. Indeed, the claim isn’t even made in the actual paper so much as in the scuttlebutt^# related to it. The scientific claim that is made is that

The halo excess spectrum can be fitted by annihilation with a particle mass $m_{χ} \sim$ 0.5–0.8 TeV and cross section $⟨ σ υ ⟩ \sim$ (5–8) $\times 10^{- 25} {cm}^{3} s^{- 1}$ for the $b \bar{b}$ channel.

Totani (2025)

What the heck does that mean?

First, the “excess spectrum” refers to a portion of the gamma ray emission detected by the Fermi telescope that exceeds that from known astrophysical sources. This signal might be from a WIMP with a mass in the range of 500 – 800 GeV. That’s a bit heavier than originally anticipated (~100 GeV), but not ridiculous. The cross-section is the probability for an interaction with bottom quarks and anti-quarks. (The Higgs boson can decay into b quarks.)

Astrophysical sources at the Galactic center

There is a long-running issue with the interpretation of excess signals as dark matter. Most of the detected emission is from known astrophysical sources, hence the term “excess.” There being an excess implies that we understand all the sources. There are a lot of astrophysical sources at the Galactic center:

The center of the Milky Way as seen by the South African MeerKAT radio telescope with a close up from JWST. Image credit: NASA, ESA, CSA, STScI, SARAO, S. Crowe (UVA), J. Bally (CU), R. Fedriani (IAA-CSIC), I. Heywood (Oxford).

As you can see, the center of the Galaxy is a busy place. It is literally the busiest place in the Galaxy. Attributing any “excess” to non-baryonic dark matter is contingent on understanding all of the astrophysical sources so that they can be correctly subtracted off. Looking at the complexity of the image above, that’s a big if, which we’ll come back to later. But first, how does dark matter even come unto a discussion of emission from the Galactic center?

Indirect WIMP detection

Dark matter does not emit light – not directly, anyway. But WIMP dark matter is hypothesized to interact with Standard Model particles through the weak nuclear force, which is what provides a window to detect it in the laboratory. So how does that work? Here is the notional Feynman diagram:

Conceivable Interactions between WIMPs (X) and standard model particles (q). The diagram can be read left to right to represent WIMPs scattering off of atomic nuclei, top to bottom to represent WIMPs annihilating into standard model particles, or bottom to top to represent the production of dark matter particles in high energy collisions.

The devious brilliance of this Feynman diagram is that we don’t need to know how the interaction works. There are many possibilities, but that’s a detail – that central circle is where the magic happens; what exactly that magic is can remain TBD. All that matters is that it can happen (with some probability quantified by the interaction cross-section), so all the pathways illustrated above should be possible.

Direct detection experiments look for scattering of WIMPs off of nuclei in underground detectors. They have not seen anything. In principle, WIMPs could be created in sufficiently high-energy collisions of Standard Model particles. The LHC has more than adequate energy to produce dark matter particles in this way, but no such signal has been seen^$. The potential signal we’re discussing here is an example of indirect detection. There are a number of possibilities for this, but the most obvious^{^} one follows from WIMPs being their own anti-particles, so they occasionally meet in space and annihilate into Standard Model particles.

The most obvious product of WIMP annihilations is a pair of gamma rays, hence the potential for the Fermi gamma ray telescope to detect their decay products. Here is a simulated image of the gamma ray sky resulting from dark matter annihilations:

*Simulated image from the via Lactea II simultion (Fig. 1 of Kuhlen et al. 2008).*

The dark regions are the brightest, where the dark matter density is highest. That includes the center of the Milky Way (white circle) and also sub-halos that might contain dwarf satellite galaxies.

Since we don’t really know how the magic interaction happens, but have plenty of theoretical variations, many other things are also possible, some of which might be cosmic rays:

Fig. 3 of Topchiev et al. (2017) illustrating possible decay channels for WIMP annihilations. Gamma rays are one inevitable product, but other particles might also be produced. These would be born with energies much higher than their rest masses (~100 GeV, while electrons and positrons have masses of 0.5 MeV) so would be moving near the speed of light. In effect, dark matter could be a source of cosmic rays.

The upshot of all this is that the detection of an “excess” of unexpected but normal particles might be a sign of dark matter.

Sociology: different perspectives from different communities

A lot hinges on the confidence with which we can disentangle expected from unexpected. Once we’ve accounted for the sources we already knew about, there are always new sources to be discovered. That’s astronomy. So initially, the communal attitude was that we shouldn’t claim a signal was due to dark matter until all astrophysical signals had been thoroughly excluded. That never happened: we just kept discovering new astrophysical sources. But at some point, the communal attitude transformed into one of eager credulity. It was no longer embarrassing to make a wrong claim; instead, marginal and dubious claims were made eagerly in the hopes of claiming a Nobel prize. If it didn’t work out, oh well, just try again. And again and again and again. There is apparently no shame in claiming to see the invisible when you’re completely convinced it is there to be seen.

This switch in sociology happened in the mid to late ’00s as people calling themselves astroparticle^& physicists became numerous. These people were remarkably uninterested in astrophysics or astrophysical sources in their own right but very interested in dark matter. They were quick to claim that any and every quirk in data was a sign of dark matter. I can’t help but wonder if this behavior is inherited from the long drought in interesting particle collider results, which gradually evolved into a propensity for high energy particle phenomenologists to leap on every two-sigma blip as a sign of new physics, dumping hundreds of preprints on arXiv after each signal of marginal significance was announced. It is always a sprint to exercise the mental model-building muscles and make up some shit in the brief weeks before the signal inevitably goes away again.

Let’s review a few examples of previous indirect dark matter detection claims.

Cosmic rays from Kaluza-Klein dark matter – or not

This topic has a long and sordid history. In the late ’00s, there were numerous claims of an excess in cosmic rays – ATIC saw too many electrons for the astrophysical background, and and PAMELA saw an apparent rise in the positron fraction, perhaps indicating a source with a peak energy around 620 GeV. (If the signal is from dark matter, the rest mass of the WIMP is imprinted in the energy spectrum of its decay products.) The combination of excess electrons and extra positrons seemed fishy enough* to some to point to new physics: dark matter. There were of course more sober analyses, for example:

Fig. 3 from Aharonian et al. (2009): The energy spectrum E³ dN/dE of cosmic-ray electrons measured by H.E.S.S. and balloon experiments. Also shown are calculations for a Kaluza-Klein signature in the H.E.S.S. data with a mass of 620 GeV and a flux as determined from the ATIC data (dashed-dotted line), the background model fitted to low-energy ATIC and high-energy H.E.S.S. data (dashed line) and the sum of the two contributions (solid line). The shaded regions represent the approximate systematic error as in Fig. 2.

A few things to note about this plot: first, the data are noisy – science is hard. The ATIC and H.E.S.S. data are not really consistent – one shows an excess, the other does not. The excess is over a background model that is overly simplistic – the high energy astrophysicists I knew were shouting that the apparent signal could easily be caused by a nearby pulsar^##. The advocates for a detection in the astroparticle community simply ignored this point, or if pressed, asserted that it seemed unlikely.

One problem that arose with the dark matter interpretation was that there wasn’t enough of it. Space is big and the dark matter density is low, so it is hard to get WIMPs together to annihilate. Indeed, the expected signal scales as the square of the WIMP density, so is very sensitive to just how much dark matter is lurking about. The average density in the solar neighborhood needed to explain astronomical data is around 0.3 to 0.4 GeV cm^-3; this falls short of producing the observed signal (if real) by a factor of ~500.

An ordinary scientist might have taken this setback as a sign that he^$$ was barking up the wrong tree. Not to be discouraged, the extraordinary astroparticle physicists started talking about the “boost factor.” If there is a region of enhanced dark matter density, then the gamma ray/cosmic ray signal would be boosted, potentially by a lot given the density-squared dependence. This is not quite as crazy as it sounds, as cold dark matter halos are predicted to be lumpy: there should be lots of sub-halos within each halo (and many sub-sub halos within those, right the way down). So, what are the odds that we happen to live near enough to a subhalo that could result in the required boost factor?

The odds are small but nonzero. I saw someone at a conference in 2009 make a completely theoretical attempt to derive those odds. He took a merger tree from some simulation and calculated the chance that we’d be near one of these lumps. Then he expanded that to include a spectrum of plausible merger trees for Milky Way-mass dark matter halos. The noisier merger histories gave higher probabilities, as halos with more recent mergers tend to be lumpier, having had a fresh injection of subhalos that haven’t had time to erode away through dynamical friction into the larger central halo.

This was all very sensible sounding, in theory – and only in theory. We don’t live in any random galaxy. We live in the Milky Way and we know quite a bit about it. One of those things is that it has had a rather quiet merger history by the standards of simulated merger trees. To be sure, there have been some mergers, like the Gaia-Enceladus Sausage. But these are few and far between compared to the expectations of the simulations our theorist was considering. Moreover, we’d know if it weren’t, because mergers tend to heat the stellar disk and puff up its thickness. The spiral disk of the Milky Way is pretty cold dynamically, which places limits on how much mass has merged and when. Indeed, there is a whole subfield dedicated to the study of the thick disk, which seems to have been puffed up in an ancient event ~8 Gyr ago. Since then it has been pretty quiet, though more subtle things can and do happen.

The speaker did not mention any of that. He had a completely theoretical depiction of the probabilities unsullied by observational evidence, and was succeeding in persuading those who wanted to believe that the small probability he came up with was nevertheless reasonable. It was a mixed audience: along with the astroparticle physicists were astronomers like myself, including one of the world’s experts on the thick disk, Rosy Wyse. However, she was too polite to call this out, so after watching the discussion devolve towards accepting the unlikely as probable, I raise my hand to comment: “We know the Milky Way’s merger history isn’t as busy as the models that give a high probability.” This was met with utter incredulity. How could astronomy teach us anything about dark matter? It’s not like the evidence is 100% astronomical in nature, or… wait, it is. But no, no waiting or self-reflection was involved. It rapidly became clear that the majority of people calling themselves astroparticle physicists were ignorant of some relevant astrophysics that any astronomy grad student would be expected to know. It just wasn’t in their training or knowledge base. Consequently, it was strange and shocking^&& for them to learn about it this way. So the discussion trended towards denial, at which point Rosy spoke up to say yes, we know this. Duh. (I paraphrase.)

The interpretation of the excess cosmic ray signal as dark matter persisted a few years, but gradually cooler heads prevailed and the pulsar interpretation became widely accepted to be more plausible – as it always had been. Indeed, claiming cosmic rays were from dark matter became almost disreputable, as it richly deserved to be. So much so that when the AMS cosmic ray experiment joined the party late, it had essentially zero impact. I didn’t hear anyone advocating for it, even in whispers at workshops. It seemed more like its Nobel laureate PI just wanted a second Nobel prize, please and thank you, and even the astroparticle community felt embarrassed for him.

This didn’t preclude the same story from playing out repeatedly.

Gamma rays from WIMPs – or not

In the lead-up to a conference on dark matter hosted at Harvard in 2014, there were claims that the Fermi telescope – the same one that is again in the news – had seen a gamma ray line around 126 GeV that was attributed to dark matter. This claim had many red flags. The mass was close to the Higgs particle mass, which was kinda weird. The signal was primarily seen on the limb of the Earth, which is exactly where you’d expect garbage noise to creep in. Most telling, the Fermi team itself was not making this claim. It came from others who were analyzing their data. I am no fan of science by big teams – they tend to become bureaucratic behemoths that create red tape for their participants and often suppress internal dissent** – but one thing they do not do is leave Nobel prizes unanalyzed in their data. The Fermi team’s silence in this matter was deafening.

In short, this first claim of gamma rays from dark matter looked to be very much on the same trajectory as that from cosmic rays. So I was somewhat surprised when I saw the draft program for the Harvard conference, as it had an entire afternoon session devoted to this topic. I wrote the organizers to politely ask if they really thought this would still be a thing by the time the conference happened. One of them was an enthusiastic proponent, so yes.

Narrator: it was not.

By the time the conference happened, the related claims had all collapsed, and all the scientists invited to speak about it talked instead about something completely different, as if it had never been a thing at all.

X-rays from sterile neutrinos – or not

Later, there was the 3.5 keV line. If one squinted really hard at X-ray data, it looked like there might sorta kinda be an unidentified line. This didn’t look particularly convincing, and there are instances when new lines have been discovered in astronomical data rather than laboratory data (e.g., helium was first recognized in the spectrum of the sun, hence the name; also nebulium, which was later recognized to be ionized oxygen), so again, one needed to consider the astrophysical possibilities.

Of course, it was much more exciting to claim it was dark matter. Never mind that it was a silly energy scale, being far too low mass to be cold dark matter (people seem to have forgotten^*# the Lee-Weinberg limit, which requires m_X > 2 GeV); a few keV is rather less than a few GeV. No matter, we can always come up with an appropriate particle – in this case, sterile neutrinos^*$.

If you’ve read this far, you can see how this was going to pan out.

Gamma rays from WIMPs again, maybe maybe

So now we have a renewed claim that the Fermi excess is dark matter. Given the history related above, the reader may appreciate that my first reaction was Really? Are we doing this again?

This is different from the claim a decade ago. The claimed mass is different, and the signal is real, being part of the mess of emission from the Galactic center. The trick, as so often the case, is disentangling the dark matter signal from the plausible astrophysical sources.

Indeed, the signal is not new, only this particular fit with WIMP dark matter is. There had, of course, been discussion of all this before, but it faded out when it became clear that the Fermi signal was well explained by a population of millisecond pulsars. Astrophysics was again the more obvious interpretation^*%. Or perhaps not: I suppose if you’re part of a community convinced that dark matter exists who is spending an enormous amount of time and resources looking for a signal from dark matter and whose basic knowledge of astrophysics extends little beyond “astronomical data show dark matter exists but are messy so there’s always room to play” then maybe invoking an invisible agent from an unknown dark sector seems just as plausible as an obvious astrophysical source. Hmmm… that would have sounded crazy to me even back when, like them, I was sure that dark matter had to exist and be made of WIMPs, but here we are.

Looking around in the literature, I see there is still a somewhat active series of papers on this subject. They split between no way and maybe.

For example, Manconi et al. (2025) show that the excess signal has the same distribution on the sky as the light from old stars in the Galaxy. The distribution of stars is asymmetrical thanks to the Galactic bar, which we see at an angle somewhere around ~30 degrees, so one end is nearer to us than the other, creating a classic “X/peanut” shape seen in other edge-on barred spiral galaxies. So not only is the spectrum of the signal consistent with millisecond pulsars, it has the same distribution on the sky as the stars from which millisecond pulsars are born. So no way is this dark matter: it is clearly an astrophysical signal.

Not to be dissuaded by such a completely devastating combination of observations, Muru et al. (2025) argue that sure, the signal looks like the stars, but the dark matter could have exactly the same distribution as the stars. They cite the Hestia simulations of the Local Group as an example where this happens. Looking at those, they’re not as unrealistic as many simulations, but they appear to suffer the common affliction of too much dark mass near the center. That leaves the dark matter more room to be non-spherical so maybe be lumpy in the same was as the stars, and also provide a higher annihilation signal from the high density of dark matter. So they say maybe, calling the pulsar and dark matter interpretations “equally compelling.”

Returning to Totani’s sort-of claimed detection, he also says

This cross section is larger than the upper limits from dwarf galaxies and the canonical thermal relic value, but considering various uncertainties, especially the density profile of the MW halo, the dark matter interpretation of the 20 GeV “Fermi halo” remains feasible.

Totani (2025)

OK, so there’s a lot to break down in this one sentence.

The canonical thermal relic value is kinda central to the whole WIMP paradigm, so needing a value higher than that is a red flag reminiscent of the need for a boost factor for the cosmic ray signal. There aren’t really enough WIMPs there to do the job unless we juice their effectiveness at making gamma rays. The juice factor is an order of magnitude here: Steigman et al. (2012) give 2.2 x 10^-26 cm³s^-1 for what the thermal cross-section should be vs. the (5-8) x 10^-25 cm³s^-1 suggested by Totani (2025).

It is also worth noting that one point of Steigman’s paper is that as a well-posed hypothesis, the WIMP cross section can be calculated; it isn’t a free parameter to play with, so needing the cross-section to be larger than the upper limits from dwarf galaxies is another red flag. If this is indeed a dark matter signal from the Galactic center, then the subhalos in which dwarf satellites reside should also be visible, as in the simulated image from via Lactea above. They are not, despite having fewer messy astrophysical signals to compete with.

So “remains feasible” is doing a lot of work here. That’s the scientific way of saying “almost certainly wrong, but maybe? Because I’d really like for it to work out that way.”

The dark matter distribution in the Milky Way

One of the critical things here is the density of dark matter near the Galactic center, as the signal scales as the square of the density. Totani (2025) simply adopts the via Lactea simulation to represent the dark matter halo of the Galaxy in his calculations. This is a reasonable choice from a purely theoretical perspective, but it is not a conservative choice for the problem at hand.

What do we know empirically? The via Lactea simulation was dark matter only. There is no stellar disk, just a dark matter halo appropriate to the Milky Way. So let’s add that halo to a baryonic mass model of the Galaxy:

*The rotation curve of the via Lactea dark matter halo (red curve) combined with the Milky Way baryon distribution (light blue line). The total rotation (dark blue line) overshoots the data.*

The important part for the Galactic center signal is the region at small radius – the first kpc or two. Like most simulations, via Lactea has a cuspy central region of high dark matter density that is inconsistent with data. This overshoots the equivalent circular velocity curve from observed stellar motions. I could fix the fit above by reducing the stellar mass, but that’s not really an option in the Milky Way – we need a maximal stellar disk to explain the microlensing rate towards the center of the Galaxy. The “various uncertainties, especially the density profile of the MW halo” statement elides this inconvenient fact. Astronomical uncertainties are ever-present, but do not favor a dark matter signal here.

We can subtract the baryonic mass model from the rotation curve data to infer what the dark matter distribution needs to be. This is done in the plot below, where it is compared to the via Lactea halo:

*The empirical dark matter halo density profile of the Milky Way (blue line) compared to the via Lactea simulation (red line).*

The empirical dark matter density profile of the Milky Way does not continue to rise inwards as steeply as the simulation predicts. It shows the same proclivity for a shallower core as pretty much every other galaxy in the sky. This reduced density of dark matter in the central couple of kpc means the signal from WIMP annihilation should be much lower than calculated from the simulated distribution. Remember – the WIMP annihilation signal scales as the square of the dark matter density, so the turn-down seen at small radii in the log-log plot above is brutal. There isn’t enough dark matter there to do what it is claimed to be doing.

Cry wolf

There have now been so many claims to detect dark matter that have come and gone that it is getting to be like the fable of the boy who cried wolf. A long series of unpersuasive claims does not inspire confidence that the next will be correct. Indeed, it has the opposite effect: it is going to be really hard to take future claims seriously.

It’s almost as if this invisible dark matter stuff doesn’t exist.

Note added: Jeff Grube points out in the comments that Wang & Duan (2025) have a recent paper showing that the dark matter signal discussed here also predicts an antiproton signal that is already excluded by AMS data. While I find this unsurprising, it is an excellent check. Indeed, it would have caused me to think again had the antiproton signal been there: independent corroboration from a separate experiment is how science is supposed to work.

^#It has become a pattern for advocates of dark matter to write a speculative paper for the journals that is fairly restrained in its claims, then hype it as an actual detection to the press. It’s like “Even I think this is probably wrong, but let’s make the claim on the off chance it pans out.”

^$Ironically, a detection from a particle collider would be a non-detection. The signature of dark matter produced in a collision would be an imbalance between the mass-energy that goes into the collision and that measured in detected particles coming out of it. The mass-energy converted into WIMPs would escape the detector undetected. This is analogous to how neutrinos were first identified, though Fermi was reluctant to make up an invisible, potentially undetectable particle – a conservative value system that modern particle physicists have abandoned. The 13,000 GeV collision energy of the LHC is more than adequate to make ~100 GeV WIMPs, so the failure of this detection mode is telling.

^{^}A less obvious possibility is spontaneous decay. This would happen if WIMPs are unstable and decay with a finite half-life. The shorter the half-life, the more decays, and the stronger the resulting signal. This implies some fine-tuning in the half-life – if it is much longer than a Hubble time, then it happens so seldom it is irrelevant; if it is shorter than a Hubble time, then dark matter halos evaporate and stable galaxies don’t exist.

^&Astroparticle physics, also known as particle astrophysics, is a relatively new field. It is also an oxymoron, being a branch of particle physics with only aspirational delusions of relevance to astrophysics. I say that to be rude to people who are rude to astronomers, but it is also true. Astrophysics is the physics of objects in the sky, and as such, requires all of physics. Physics is a broad field, so some aspects are more relevant than others. When I teach a survey course, it touches on gravity, electromagnetism, atomic and molecular quantum mechanics, nuclear physics, and with the discovery of exoplanets, increasingly on geophysics. Particle physics doesn’t come up. It’s just not relevant, except where it overlaps with nuclear physics. (As poorly as particle physicists think of astronomers, they seem to think even less of nuclear physicists, whom they consider to be failed particle physicists (if only they were smart enough!) and nuclear physicists hate them in return.) This new field of astroparticle physics seems to be all about dark matter as driven by early universe cosmology, with contempt for everything that happens in the 13 billion years following the production of the relic radiation seen as the microwave background. Anything later is dismissed as mere “gastrophysics” that is too complicated to understand so cannot possibly inform fundamental physics. I guess that’s true if one chooses to remain ignorant of it.

*Fishy results can also indicate something fishy with the data. I had a conversation with an instrument builder at the time who pointed out that PAMELA had chosen to fly without a particular discriminator in order to save weight; he suggested that its absence could explain the apparent upturn in positrons.

^##There is a relatively nearby pulsar that fits the bill. It has a name: Geminga. This illustrates the human tendency to see what we’re looking for. The astroparticle community was looking for dark matter, so that’s what many of them saw in the excess cosmic ray signal. High energy astrophysicists work on neutron stars, so the obvious interpretation to them was a pulsar. One I recall being particularly scornful of the dark matter interpretation when there was an obvious astrophysical source. I also remember the astroparticle people being quick to dismiss the pulsar interpretation because it seemed unlikely to them for one to be so close but really they hadn’t thought about it before: that pulsars could do this was news to them, and many preferred to believe the dark matter interpretation.

^$$All the people barking were men.

^&&This experience opened my eyes to the existence of an entire community of scientists who were working on dark matter in somewhat gratuitous ignorance of the astronomical evidence for dark matter. To them, the existence of the stuff had already been demonstrated; the interesting thing now was to find the responsible particle. But they were clearly missing many important ingredients – another example is disk stability, a foundational reason to invoke dark matter that seems to routinely come as a surprise to particle physicists. This disconnect is part of what motivated me to develop an entire semester course on dark matter, which I’ve taught every other year since 2013 and will teach again this coming semester. The first time I taught it, I worried that there wasn’t enough material for a whole semester. Now a semester isn’t enough time.

**I had a college friend (sadly now deceased) who was part of the team that discovered the Higgs. That was big business, to the extent that there were two experiments – one to claim the detection, and another on the same beam to do the confirmation. The first experiment exceeded the arbitrary 5σ threshold to claim a 5.2σ detection, but the second only reached 4.9σ. So, in all appropriateness, he asked in a meeting if they could/should really announce a detection. A Nobel prize was on the line, so the answer was straightforward: Do you want a detection or not? (His words.)

^*#Rather than forget, some choose to fiddle ways around the Lee-Weinberg limit. This has led to the sub-genre of “light dark matter” which means lightweight, not luminous. I’d say this was the worst name ever, but the same people talk about dark photons with a straight face, so irony continues to bleed out.

^*$Ironically, a sterile neutrino has also been invoked to address problems in MOND.

^*%I was amused once to see one of the more rabid advocates of dark matter signals of this type give an entire talk hyping the various possibilities only to mention pulsars at the end with a sigh, admitting that the Fermi signal looked exactly like that.

What if we never find dark matter?

Some people have asked me to comment on the Scientific American article What if We Never Find Dark Matter? by Slatyer & Tait. For the most part, I find it unobjectionable – from a certain point of view. It is revealing to examine this point of view, starting with the title, which frames the subject in a way that gives us permission to believe in dark matter while never finding it. This framing is profoundly unscientific, as it invites a form of magical thinking that could usher in a thousand years of dark epicycles (feedback being the modern epicycle) on top of the decades it has already sustained.

The article does recognize that a modification of gravity is at least a logical possibility. The mere mention of this is progress, if grudging and slow. They can’t bring themselves to name a specific theory: they never say MOND and only allude obliquely to a single relativistic theory as if saying its name out loud would bring a curse^% upon their house.

Of course, they mention modified gravity merely to dismiss it:

A universe without dark matter would require striking modifications to the laws of gravity… [which] seems exceptionally difficult.

Yes it is. But it has also proven exceptionally difficult to detect dark matter. That hasn’t stopped people from making valiant efforts to do so. So the argument is that we should try really hard to accomplish the exceptionally difficult task of detecting dark matter, but we shouldn’t bother trying to modify gravity because doing so would be exceptionally difficult.

This speaks to motivations – is one idea better motivated? In the 1980s, cold dark matter was motivated by both astronomical observations and physical theory. Absent the radical thought of modifying gravity, we had a clear need for unseen mass. Some of that unseen mass could simply have been undetected normal matter, but most of it needed to be some form of non-baryonic dark matter that exceeded the baryon density allowed by Big Bang Nucleosynthesis and did not interact directly with photons. That meant entirely new physics from beyond the Standard Model of particle physics: no particle in the known stable of particles suffices. This new physics was seen as a good thing, because particle physicists already had the feeling that there should be something more than the Standard Model. There was a desire for Grand Unified Theories (GUTs) and supersymmetry (SUSY). SUSY naturally provides a home for particles that could be the dark matter, in particular the Weakly Interacting Massive Particles (WIMPs) that are the prime target for the vast majority of experiments that are working to achieve the exceptionally difficult task of detecting them. So there was a confluence of reasons from very different perspectives to make the search for WIMPs very well motivated.

That was then. Fast forward a few decades, and the search for WIMPs has failed. Repeatedly. Continuing to pursue it is an example of the sunk cost fallacy. We keep doing it because we’ve already done so much of it that surely we should keep going. So I feel the need to comment on this seemingly innocuous remark:

although many versions of supersymmetry predict WIMP dark matter, the converse isn’t true; WIMPs are viable dark matter candidates even in a universe without supersymmetry.

Strictly speaking, this is correct. It is also weak sauce. The neutrino is an example of a weakly interacting particle that has some mass. We know neutrinos exist, and they reside in the Standard Model – no need for supersymmetry. We also know that they cannot be the dark matter, so it would be disingenuous to conflate the two. Beyond that, it is possible to imagine a practically infinite variety of particles that are weakly interacting by not part of supersymmetry. That’s just throwing mud at the wall. SUSY WIMPs were extraordinarily well motivated, with the WIMP miracle being the beautiful argument that launched a thousand experiments. But lacking SUSY – which seems practically dead at this juncture – WIMPS as originally motivated are dead along with it. The motivation for more generic WIMPs is lacking, so the above statement is nothing more than an assertion that runs interference for the fact that we no longer have good reason to expect WIMPs at all.

There is also an element of disciplinary-centric thinking: if you’re a particle physicist, you can build a dark matter detector and maybe make a major discovery or at least get great gobs of grants in the effort to do so. If instead what is going on is really a modification of gravity, then your expertise is irrelevant and there is no reason to keep shoveling money into your field. Worse, a career spent at the bottom of a mine shaft working on dark matter detectors is a waste of effort. I can understand why people don’t want to hear that message, but that just brings us back to the sunk cost fallacy.

Speaking of money, I occasionally get scientists who come up to me Big Mad that grant money gets spent on MOND research, as that would be a waste of taxpayer money. I can assure them that no government dollars have been harmed in the pursuit of MOND research. Certainly not in the U.S., at any rate. But lots and lots of tax dollars have been burned in the search for dark matter, and the article we’re discussing advocates spending a whole lot more to search for dark matter candidates that are nowhere near as well motivated as WIMPs were. That’s why I keep asking: how do we know when to stop? I don’t expect other scientists to agree to my interpretation of the data, but I do expect them to have a criterion whereby they would accede that dark matter is incorrect. If we lack any notion of how we could figure out that we are wrong, then we’ve made the leap from science to religion. So far, such criteria are sadly lacking, and I see precious little evidence of people rising to the challenge. Indeed, I frequently get the opposite, as other scientists have frequently asserted to me that they would only consider MOND as a last resort. OK, when does that happen? There’s always another particle we can think up, so the answer seems to be “never.”

I wrote long ago that “After WIMPs, the next obvious candidate is axions.” Sure enough, this article spills a lot of ink discussing axions. Rather than dwell on this different doomed idea for dark matter, let’s take a gander at the remarkable art made to accompany the article, because we are visual animals and graphical representations are important.

Where to start? Right in the center is a scroll of an old-timey star chart. On top of that are several depictions of what I guess are meant to be galaxies*. Around those is an ethereal dragon representing the unknown dark matter. The depiction of dark matter as an unfathomable monster is at once both spot on and weirdly anthropomorphic. Is this a fabled beast the adventurous hero is supposed to seek out and slay? or befriend? or maybe it is a tale in which he grows during the journey to realize he has been on the wrong path the whole time? I love the dragon as art, but as a representation of a scientific subject it imparts an aura of teleological biology to something that is literally out of this world, residing in a dark sector that is not part of our daily experience and may be entirely inaccessible to our terrestrial experimentation. Off the edge of the map and on into extra dimensions: here there be monsters.

The representations here are fantastic. There is the coffee mug and the candle to represent the hard work of those of us who burn the candle at both ends wrestling with the dark matter problem. There’s a magnifying glass to represent how hard the experimentalists have looked for the dark matter. Scattered around are various totems, like the Polaroid-style picture at right depicting the gravitational lensing around a black hole. This is cool, but has squat to do with the missing mass problem. It’s more a nod to General Relativity and the Faith we have therein, albeit in a regime many orders of magnitude removed from the one that concerns us here. On the left is an old newspaper article about WIMPs, complete with a sketch of a Feynman diagram that depicts how we might detect them. And at the top, peeking out of a book, as it were a thought made long ago now seeking new relevance, a note saying Axions!

I can save everyone a lot of time, effort, and expense. It ain’t WIMPs and it ain’t axions. Nor is the dark matter any of the plethora of other ideas illustrated in the eye-watering depiction of the landscape of particle possibilities in the article. These simply add mass while providing no explanation of the observed MOND phenomenology. This phenomenology is fundamental to the problem, so any approach that ignores it is doomed to failure. I’m happy to consider explanations based on dark matter, but these need to have a direct connection to baryons baked-in to be viable. None of the ideas they discuss meet this minimum criterion.

Of course it could be that MOND – either as modified gravity or modified inertia, an important possibility that usually gets overlooked – is essentially correct and that’s why it keeps having predictions come true. That’s what motivates considering it now: repeated and sustained predictive success, particularly for phenomena that dark matter does not provide a satisfactory explanation for.

Of course, this article advocating dark matter is at pains to dismiss modified gravity as a possibility:

The changes [of modified gravity] would have to mimic the effects of dark matter in astrophysical systems ranging from giant clusters of galaxies to the Milky Way’s smallest satellite galaxies. In other words, they would need to apply across an enormous range of scales in distance and time, without contradicting the host of other precise measurements we’ve gathered about how gravity works. The modifications would also need to explain why, if dark matter is just a modification to gravity—which is universally associated with all matter—not all galaxies and clusters appear to contain dark matter. Moreover, the most sophisticated attempts to formulate self-consistent theories of modified gravity to explain away dark matter end up invoking a type of dark matter anyway, to match the ripples we observe in the cosmic microwave background, leftover light from the big bang.

That’s a lot, so let’s break it down. First, that modified gravity “would have to mimic the effects of dark matter” gets it exactly backwards. It is dark matter that has to mimic the effects of MOND. That’s an easy call: dark matter plus baryons could combine in a large variety of ways that might bear no resemblance to MOND. Indeed, they should do that: the obvious prediction of LCDM-like theories is an exponential disk in an NFW halo. In contrast, there is one and only one thing that can happen in MOND since there is a single effective force law that connects the dynamics to the observed distribution of baryons. Galaxies didn’t have to do that, shouldn’t do that, but remarkably they do. The uniqueness of this relation poses a problem for dark matter that has been known since the previous century:

*Reluctant conclusions from McGaugh & de Blok (1998). As we said at the time, “This result surprised the bejeepers out of us, too.”*

This basic conclusion has not changed over the years, only gotten stronger. The equation coupling dark to luminous matter I wrote down in all generality in McGaugh (2004) and again in McGaugh et al. (2016). The latter paper is published in Physical Review Letters, arguably the most prominent physics journal, and is in the top percentile of citation rates, so it isn’t some minuscule detail buried in an obscure astronomical journal that might have eluded the attention of particle physicists. It is the implication that conclusion [1] could be correct that bounces off a protective shell of cognitive dissonance so hard that the necessary corollary [2] gets overlooked.

OK, that’s just the first sentence. Let’s carry on with “[the modification] would need to apply across an enormous range of scales in distance and time, without contradicting the host of other precise measurements we’ve gathered about how gravity works.” Well, duh. That’s the first thing I checked. Thoroughly and repeatedly. I’ve written many reviews on the subject. They’re either unaware of some well-established results, or choose to ignore them.

The reason MOND doesn’t contradict the host of other constraints about how gravity works is simple. It happens in the low acceleration regime, where the only test of gravity is provided by the data that evince the mass discrepancy. If we had posed galaxy observations as a test of GR, we would have concluded that it fails at low accelerations. Of course we didn’t do that; we observed galaxies because we were interested in how they worked, then inferred the need for dark matter when gravity as we currently know it failed to explain the data. Other tests, regardless how precise, are irrelevant if they probe accelerations higher than Milgrom’s constant (1.2 x 10^-10 m/s/s).

Continuing on, there is the complaint that “modifications would also need to explain why… not all galaxies and clusters appear to contain dark matter.” Yep, you gotta explain all the data. That starts with the vast majority of the data that do follow the radial acceleration relation, which is not satisfactorily explained by dark matter. They skip⁺ past that part, preferring to ignore the forest in order to complain about a few outlying trees. There are some interesting cases, to be sure, but this complaint about objects lacking dark matter is misplaced for deeper reasons. It makes no sense in terms of dark matter that there are objects without dark matter. That shouldn’t happen in LCDM any more than in MOND^$. One winds up invoking non-equilibrium effects, which we can do in MOND just as we do in dark matter. It is not satisfactory in either case, but it is weird to complain about it for one theory while not for the other. This line of argument is perilously close to the a priori fallacy.

The last line, “the most sophisticated attempts to formulate self-consistent theories of modified gravity to explain away dark matter end up invoking a type of dark matter anyway, to match the ripples we observe in the cosmic microwave background” actually has some merit. The theory they’re talking about is Aether-Scalar-Tensor (AeST) theory, which I guess earns the badge of “most sophisticated” because it fits the power spectrum of the cosmic microwave background (CMB).

I’ve discussed the CMB in detail before, so won’t belabor it here. I will note that the microwave background is only one piece of many lines of evidence, and the conclusion one reaches depends on how one chooses to weigh the various incommensurate evidence. That they choose to emphasize this one thing while entirely eliding the predictive successes of MOND is typical, but does not encourage me to take this as a serious argument, especially when I had more success predicting important aspects of the microwave background than did the entire community that persistently cites the microwave background to the exclusion of all else.

It is also a bit strange to complain that AeST “explain[s] away dark matter [but] end[s] up invoking a type of dark matter.” I think what they mean here is true at the level of quantum field theory where all particles are fields and all fields are particles, but beyond that, they aren’t the same thing at all. It is common for modified gravity theories to invoke scalar fields^#, and this is an important degree of freedom that enables AeST to fit the CMB. TeVeS also added a scalar and tensor field, but could not fit the CMB, so this approach isn’t guaranteed to work. But are these a type of dark matter? Or are our ideas of dark matter mimicking a scalar field? It seems like this argument could cut either way, and we’re just granting dark matter priority as a concept because we thought of it first. I don’t think nature cares about the order of our thoughts.

None of this addresses the question of the year. Why does MOND get any predictions right? Just saying “dark matter does it” is not sufficient. Until scientists engage seriously with this question, they’re doomed to chasing phantoms that aren’t there to catch.

^%From what I’ve seen, they’re probably right to fear the curses of their colleagues for such blasphemy. Very objective, very scientific.

*Galaxies are nature’s artwork; human imitations never seem adequate. These look more like fried eggs to me. On the whole, this art is exceptionally well informed by science, or at least by particle physics, but not so much by astronomy. And therein lies the greater problem: there is a whole field of physics devoted to dark matter that is entirely motivated by astronomical observations yet its practitioners are, by and large, remarkably ignorant of anything more than the most rudimentary aspects of the data that motivate their field’s existence.

⁺There seems to be a common misconception that anything we observe is automatically explained by dark matter. That’s only true at the level of inference: any excess gravity is attributable to unseen mass. That’s why a hypothesis is only as good as its prior; a mere inference isn’t science, you have to make a prediction. Once you do that, you find dark matter might do lots of things that are not at all like the MONDian phenomenology that we observe. While I would hope the need for predictions is obvious, many scientists seem to conflate observation with prediction – if we observe it, that’s what dark matter must predict!

^$The discrepancy should only appear below the critical acceleration scale in MOND. So strictly speaking, MOND does predict that there should be objects without dark matter: systems that are high acceleration. The central regions of globular clusters and elliptical galaxies are such regions, and MOND fares well there. In contrast, it is rather hard to build a sensible dark matter model that is as baryon dominated as observed. So this is an example of MOND explaining the absence of dark matter better than dark matter theory. This is related to the observation that the apparent need for dark matter only appears at low accelerations, at a scale that dark matter knows nothing about.

^#I, personally, am skeptical of this approach, as it seems too generic (let’s add some new freedom!) when it feels like we’re missing something fundamental, perhaps along the lines of Mach’s Principle. However, I also recognize that this is a feeling on my part; it is outside my training to have a meaningful opinion.

What we have here is a failure to communicate

Kuhn noted that as paradigms reach their breaking point, there is a divergence of opinions between scientists about what the important evidence is, or what even counts as evidence. This has come to pass in the debate over whether dark matter or modified gravity is a better interpretation of the acceleration discrepancy problem. It sometimes feels like we’re speaking about different topics in a different language. That’s why I split the diagram version of the dark matter tree as I did:

*Evidence indicating acceleration discrepancies in the universe and various flavors of hypothesized solutions.*

Astroparticle physicists seem to be well-informed about the cosmological evidence (top) and favor solutions in the particle sector (left). As more of these people entered the field in the ’00s and began attending conferences where we overlapped, I recognized gaping holes in their knowledge about the dynamical evidence (bottom) and related hypotheses (right). This was part of my motivation to develop an evidence-based course¹ on dark matter, to try to fill in the gaps in essential knowledge that were obviously being missed in the typical graduate physics curriculum. Though popular on my campus, not everyone in the field has the opportunity to take this course. It seems that the chasm has continued to grow, though not for lack of attempts at communication.

Part of the problem is a phase difference: many of the questions that concern astroparticle physicists (structure formation is a big one) were addressed 20 years ago in MOND. There is also a difference in texture: dark matter rarely predicts things but always explains them, even if it doesn’t. MOND often nails some predictions but leaves other things unexplained – just a complete blank. So they’re asking questions that are either way behind the curve or as-yet unanswerable. Progress rarely follows a smooth progression in linear time.

I have become aware of a common construction among many advocates of dark matter to criticize “MOND people.” First, I don’t know what a “MOND person” is. I am a scientist who works on a number of topics, among them both dark matter and MOND. I imagine the latter makes me a “MOND person,” though I still don’t really know what that means. It seems to be a generic straw man. Users of this term consistently paint such a luridly ridiculous picture of what MOND people do or do not do that I don’t recognize it as a legitimate depiction of myself or of any of the people I’ve met who work on MOND. I am left to wonder, who are these “MOND people”? They sound very bad. Are there any here in the room with us?

I am under no illusions as to what these people likely say when I am out of ear shot. Someone recently pointed me to a comment on Peter Woit’s blog that I would not have come across on my own. I am specifically named. Here is a screen shot:

*From a reply to a post of Peter Woit on December 8, 2022. I omit the part about right-handed neutrinos as irrelevant to the discussion here.*

This concisely pinpoints where the field² is at, both right and wrong. Let’s break it down.

let me just remind everyone that the primary reason to believe in the phenomenon of cold dark matter is the very high precision with which we measure the CMB power spectrum, especially modes beyond the second acoustic peak

This is correct, but it is not the original reason to believe in CDM. The history of the subject matters, as we already believed in CDM quite firmly before any modes of the acoustic power spectrum of the CMB were measured. The original reasons to believe in cold dark matter were (1) that the measured, gravitating mass density exceeds the mass density of baryons as indicated by BBN, so there is stuff out there with mass that is not normal matter, and (2) large scale structure has grown by a factor of 10⁵ from the very smooth initial condition indicated initially by the nondetection of fluctuations in the CMB, while normal matter (with normal gravity) can only get us a factor of 10³ (there were upper limits excluding this before there was a detection). Structure formation additionally imposes the requirement that whatever the dark matter is moves slowly (hence “cold”) and does not interact via electromagnetism in order to evade making too big an impact on the fluctuations in the CMB (hence the need, again, for something non-baryonic).

When cold dark matter became accepted as the dominant paradigm, fluctuations in the CMB had not yet been measured. The absence of observable fluctuations at a larger level sufficed to indicate the need for CDM. This, together with Ω_m > Ω_b from BBN (which seemed the better of the two arguments at the time), sufficed to convince me, along with most everyone else who was interested in the problem, that the answer had³ to be CDM.

This all happened before the first fluctuations were observed by COBE in 1992. By that time, we already believed firmly in CDM. The COBE observations caused initial confusion and great consternation – it was too much! We actually had a prediction from then-standard SCDM, and it had predicted an even lower level of fluctuations than what COBE observed. This did not cause us (including me) to doubt CDM (thought there was one suggestion that it might be due to self-interacting dark matter); it seemed a mere puzzle to accommodate, not an anomaly. And accommodate it we did: the power in the large scale fluctuations observed by COBE is part of how we got LCDM, albeit only a modest part. A lot of younger scientists seem to have been taught that the power spectrum is some incredibly successful prediction of CDM when in fact it has surprised us at nearly every turn.

As I’ve related here before, it wasn’t until the end of the century that CMB observations became precise enough to provide a test that might distinguish between CDM and MOND. That test initially came out in favor of MOND – or at least in favor of the absence of dark matter: No-CDM, which I had suggested as a proxy for MOND. Cosmologists and dark matter advocates consistently omit this part of the history of the subject.

I had hoped that cosmologists would experience the same surprise and doubt and reevaluation that I had experienced when MOND cropped up in my own data when it cropped up in theirs. Instead, they went into denial, ignoring the successful prediction of the first-to-second peak amplitude ratio, or, worse, making up stories that it hadn’t happened. Indeed, the amplitude of the second peak was so surprising that the first paper to measure it omitted mention of it entirely. Just didn’t talk about it, let alone admit that “Gee, this crazy prediction came true!” as I had with MOND in LSB galaxies. Consequently, I decided that it was better to spend my time working on topics where progress could be made. This is why most of my work on the CMB predates “modes beyond the second peak” just as our strong belief in CDM also predated that evidence. Indeed, communal belief in CDM was undimmed when the modes defining the second peak were observed, despite the No-CDM proxy for MOND being the only hypothesis to correctly predict it quantitatively a priori.

That said, I agree with clayton’s assessment that

CDM thinks [the second and third peak] should be about the same

That this is the best evidence now is both correct and a much weaker argument than it is made out to be. It sounds really strong, because a formal fit to the CMB data require a dark matter component at extremely high confidence – something approaching 100 sigma. This analysis assumes that dark matter exist. It does not contemplate that something else might cause the same effect, so all it really does, yet again, is demonstrate that General Relativity cannot explain cosmology when restricted to the material entities we concretely know to exist.

Given the timing, the third peak was not a strong element of my original prediction, as we did not yet have either a first or second peak. We hadn’t yet clearly observed peaks at all, so what I was doing was pretty far-sighted, but I wasn’t thinking that far ahead. However, the natural prediction for the No-CDM picture I was considering was indeed that the third peak should be lower than the second, as I’ve discussed before.

The No-CDM model (blue line) that correctly predicted the amplitude of the second peak fails to predict that of the third. Data from the Planck satellite; model line from McGaugh (2004); figure from McGaugh (2015).

In contrast, in CDM, the acoustic power spectrum of the CMB can do a wide variety of things:

*Acoustic power spectra calculated for the CMB for a variety of cosmic parameters. From Dodelson & Hu (2002).*

Given the diversity of possibilities illustrated here, there was never any doubt that a model could be fit to the data, provided that oscillations were observed as expected in any of the theories under consideration here. Consequently, I do not find fits to the data, though excellent, to be anywhere near as impressive as commonly portrayed. What does impress me is consistency with independent data.

What impresses me even more are a priori predictions. These are the gold standard of the scientific method. That’s why I worked my younger self’s tail off to make a prediction for the second peak before the data came out. In order to make a clean test, you need to know what both theories predict, so I did this for both LCDM and No-CDM. Here are the peak ratios predicted before there were data to constrain them, together with the data that came after:

*The ratio of the first-to-second (left) and second-to-third peak (right) amplitude ratio in LCDM (red) and No-CDM (blue) as predicted by Ostriker & Steinhardt (1995) and McGaugh (1999)*. Subsequent data as labeled.

The left hand panel shows the predicted amplitude ratio of the first-to-second peak, A_1:2. This is the primary quantity that I predicted for both paradigms. There is a clear distinction between the predicted bands. I was not unique in my prediction for LCDM; the same thing can be seen in other contemporaneous models. All contemporaneous models. I was the only one who was not surprised by the data when they came in, as I was the only one who had considered the model that got the prediction right: No-CDM.

The same No-CDM model fails to correctly predict the second-to-third peak ratio, A_2:3. It is, in fact, way off, while LCDM is consistent with A_2:3, just as Clayton says. This is a strong argument against No-CDM, because No-CDM makes a clear and unequivocal prediction that it gets wrong. Clayton calls this

a stone-cold, qualitative, crystal clear prediction of CDM

which is true. It is also qualitative, so I call it weak sauce. LCDM could be made to fit a very large range of A_2:3, but it had already got A_1:2 wrong. We had to adjust the baryon density outside the allowed range in order to make it consistent with the CMB data. The generous upper limit that LCDM might conceivably have predicted in advance of the CMB data was A_1:2 < 2.06, which is still clearly less than observed. For the first years of the century, the attitude was that BBN had been close, but not quite right – preference being given to the value needed to fit the CMB. Nowadays, BBN and the CMB are said to be in great concordance, but this is only true if one restricts oneself to deuterium measurements obtained after the “right” answer was known from the CMB. Prior to that, practically all of the measurements for all of the important isotopes of the light elements, deuterium, helium, and lithium, all concurred that the baryon density Ω_bh² < 0.02, with the consensus value being Ω_bh² = 0.0125 ± 0.0005. This is barely half the value subsequently required to fit the CMB (Ω_bh² = 0.0224 ± 0.0001). But what’s a factor of two among cosmologists? (In this case, 4 sigma.)

Taking the data at face value, the original prediction of LCDM was falsified by the second peak. But, no problem, we can move the goal posts, in this case by increasing the baryon density. The successful prediction of the third peak only comes after the goal posts have been moved to accommodate the second peak. Citing only the comparable size of third peak to the second while not acknowledging that the second was too small elides the critical fact that No-CDM got something right, a priori, that LCDM did not. No-CDM failed only after LCDM had already failed. The difference is that I acknowledge its failure while cosmologists elide this inconvenient detail. Perhaps the second peak amplitude is a fluke, but it was a unique prediction that was exactly nailed and remains true in all subsequent data. That’s a pretty remarkable fluke⁴.

LCDM wins ugly here by virtue of its flexibility. It has greater freedom to fit the data – any of the models in the figure of Dodelson & Hu will do. In contrast. No-CDM is the single blue line in my figure above, and nothing else. Plausible variations in the baryon density make hardly any difference: A_1:2 has to have the value that was subsequently observed, and no other. It passed that test with flying colors. It flunked the subsequent test posed by A_2:3. For LCDM this isn’t even a test, it is an exercise in fitting the data with a model that has enough parameters⁵ to do so.

There were a number of years at the beginning of the century during which the No-CDM prediction for the A_1:2 was repeatedly confirmed by multiple independent experiments, but before the third peak was convincingly detected. During this time, cosmologists exhibited the same attitude that Clayton displays here: the answer has to be CDM! This warrants mention because the evidence Clayton cites did not yet exist. Clearly the as-yet unobserved third peak was not the deciding factor.

In those days, when No-CDM was the only correct a priori prediction, I would point out to cosmologists that it had got A_1:2 right when I got the chance (which was rarely: I was invited to plenty of conferences in those days, but none on the CMB). The typical reaction was usually outright denial⁶ though sometimes it warranted a dismissive “That’s not a MOND prediction.” The latter is a fair criticism. No-CDM is just General Relativity without CDM. It represented MOND as a proxy under the ansatz that MOND effects had not yet manifested in a way that affected the CMB. I expected that this ansatz would fail at some point, and discussed some of the ways that this should happen. One that’s relevant today is that galaxies form early in MOND, so reionization happens early, and the amplitude of gravitational lensing effects is amplified. There is evidence for both of these now. What I did not anticipate was a departure from a damping spectrum around L=600 (between the second and third peaks). That’s a clear deviation from the prediction, which falsifies the ansatz but not MOND itself. After all, they were correct in noting that this wasn’t a MOND prediction per se, just a proxy. MOND, like Newtonian dynamics before it, is relativity adjacent, but not itself a relativistic theory. Neither can explain the CMB on their own. If you find that an unsatisfactory answer, imagine how I feel.

The same people who complained then that No-CDM wasn’t a real MOND prediction now want to hold MOND to the No-CDM predicted power spectrum and nothing else. First it was the second peak isn’t a real MOND prediction! then when the third peak was observed it became no way MOND can do this! This isn’t just hypocritical, it is bad science. The obvious way to proceed would be to build on the theory that had the greater, if incomplete, predictive success. Instead, the reaction has consistently been to cherry-pick the subset of facts that precludes the need for serious rethinking.

This brings us to sociology, so let’s examine some more of what Clayton has to say:

Any talk I’ve ever seen by McGaugh (or more exotic modified gravity people like Verlinde) elides this fact, and they evade the questions when I put my hand up to ask. I have invited McGaugh to a conference before specifically to discuss this point, and he just doesn’t want to.

Now you’re getting persona l .

There is so much to unpack here, I hardly know where to start. By saying I “elide this fact” about the qualitatively equality of the second and third peak, Clayton is basically accusing me of lying by omission. This is pretty rich coming from a community that consistently elides the history I relate above, and never addresses the question raised by MOND’s predictive power.

Intellectual honesty is very important to me – being honest that MOND predicted what I saw in low surface brightness where my own prediction was wrong is what got me into this mess in the first place. It would have been vastly more convenient to pretend that I never heard of MOND (at first I hadn’t⁷) and act like that never happened. That would be an lie of omission. It would be a large lie, a lie that denies an important aspect of how the world works (what we’re supposed to uncover through science), the sort of lie that cleric Paul Gerhardt may have had in mind when he said

When a man lies, he murders some part of the world.
Paul Gerhardt

Clayton is, in essence, accusing me of exactly that by failing to mention the CMB in talks he has seen. That might be true – I give a lot of talks. He hasn’t been to most of them, and I usually talk about things I’ve done more recently than 2004. I’ve commented explicitly on this complaint before –

There’s only so much you can address in a half hour talk. [This is a recurring problem. No matter what I say, there always seems to be someone who asks “why didn’t you address X?” where X is usually that person’s pet topic. Usually I could do so, but not in the time allotted.]

– so you may appreciate my exasperation at being accused of dishonesty by someone whose complaint is so predictable that I’ve complained before about people who make this complaint. I’m only human – I can’t cover all subjects for all audiences every time all the time. Moreover, I do tend to choose to discuss subjects that may be news to an audience, not simply reprise the greatest hits they want to hear. Clayton obviously knows about the third peak; he doesn’t need to hear about it from me. This is the scientific equivalent of shouting Freebird! at a concert.

It isn’t like I haven’t talked about it. I have been rigorously honest about the CMB, and certainly have not omitted mention of the third peak. Here is a comment from February 2003 when the third peak was only tentatively detected:

Page et al. (2003) do not offer a WMAP measurement of the third peak. They do quote a compilation of other experiments by Wang et al. (2003). Taking this number at face value, the second to third peak amplitude ratio is A_2:3 = 1.03 +/- 0.20. The LCDM expectation value for this quantity was 1.1, while the No-CDM expectation was 1.9. By this measure, LCDM is clearly preferable, in contradiction to the better measured first-to-second peak ratio.

Or here, in March 2006:

the Boomerang data and the last credible point in the 3-year WMAP data both have power that is clearly in excess of the no-CDM prediction. The most natural interpretation of this observation is forcing by a mass component that does not interact with photons, such as non-baryonic cold dark matter.

There are lots like this, including my review for CJP and this talk given at KITP where I had been asked to explicitly take the side of MOND in a debate format for an audience of largely particle physicists. The CMB, including the third peak, appears on the fourth slide, which is right up front, not being elided at all. In the first slide, I tried to encapsulate the attitudes of both sides:

I did the same at a meeting in Stony Brook where I got a weird vibe from the audience; they seemed to think I was lying about the history of the second peak that I recount above. It will be hard to agree on an interpretation if we can’t agree on documented historical facts.

More recently, this image appears on slide 9 of this lecture from the cosmology course I just taught (Fall 2022):

I recognize this slide from talks I’ve given over the past five plus years; this class is the most recent place I’ve used it, not the first. On some occasions I wrote “The 3rd peak is the best evidence for CDM.” I do not recall which all talks I used this in; many of them were likely colloquia for physics departments where one has more time to cover things than in a typical conference talk. Regardless, these apparently were not the talks that Clayton attended. Rather than it being the case that I never address this subject, the more conservative interpretation of the experience he relates would be that I happened not to address it in the small subset of talks that he happened to attend.

But do go off, dude: tell everyone how I never address this issue and evade questions about it.

I have been extraordinarily patient with this sort of thing, but I confess to a great deal of exasperation at the perpetual whataboutism that many scientists engage in. It is used reflexively to shut down discussion of alternatives: dark matter has to be right for this reason (here the CMB); nothing else matters (galaxy dynamics), so we should forbid discussion of MOND. Even if dark matter proves to be correct, the CMB is being used an excuse to not address the question of the century: why does MOND get so many predictions right? Any scientist with a decent physical intuition who takes the time to rub two brain cells together in contemplation of this question will realize that there is something important going on that simply invoking dark matter does not address.

In fairness to McGaugh, he pointed out some very interesting features of galactic DM distributions that do deserve answers. But it turns out that there are a plurality of possibilities, from complex DM physics (self interactions) to unmodelable SM physics (stellar feedback, galaxy-galaxy interactions). There are no such alternatives to CDM to explain the CMB power spectrum.

Thanks. This is nice, and why I say it would be easier to just pretend to never have heard of MOND. Indeed, this succinctly describes the trajectory I was on before I became aware of MOND. I would prefer to be recognized for my own work – of which there is plenty – than an association with a theory that is not my own – an association that is born of honestly reporting a surprising observation. I find my reception to be more favorable if I just talk about the data, but what is the point of taking data if we don’t test the hypotheses?

I have gone to great extremes to consider all the possibilities. There is not a plurality of viable possibilities; most of these things do not work. The specific ideas that are cited here are known not work. SIDM apears to work because it has more free parameters than are required to describe the data. This is a common failing of dark matter models that simply fit some functional form to observed rotation curves. They can be made to fit the data, but they cannot be used to predict the way MOND can.

Feedback is even worse. Never mind the details of specific feedback models, and think about what is being said here: the observations are to be explained by “unmodelable [standard model] physics.” This is a way of saying that dark matter claims to explain the phenomena while declining to make a prediction. Don’t worry – it’ll work out! How can that be considered better than or even equivalent to MOND when many of the problems we invoke feedback to solve are caused by the predictions of MOND coming true? We’re just invoking unmodelable physics as a deus ex machina to make dark matter models look like something they are not. Are physicists straight-up asserting that it is better to have a theory that is unmodelable than one that makes predictions that come true?

Returning to the CMB, are there no “alternatives to CDM to explain the CMB power spectrum”? I certainly do not know how to explain the third peak with the No-CDM ansatz. For that we need a relativistic theory, like Bekenstein‘s TeVeS. This initially seemed promising, as it solved the long-standing problem of gravitational lensing in MOND. However, it quickly became clear that it did not work for the CMB. Nevertheless, I learned from this that there could be more to the CMB oscillations than allowed by the simple No-CDM ansatz. The scalar field (an entity theorists love to introduce) in TeVeS-like theories could play a role analogous to cold dark matter in the oscillation equations. That means that what I thought was a killer argument against MOND – the exact same argument Clayton is making – is not as absolute as I had thought.

Writing down a new relativistic theory is not trivial. It is not what I do. I am an observational astronomer. I only play at theory when I can’t get telescope time.

*Comic from the Far Side by Gary Larson*.

So in the mid-00’s, I decided to let theorists do theory and started the first steps in what would ultimately become the SPARC database (it took a decade and a lot of effort by Jim Schombert and Federico Lelli in addition to myself). On the theoretical side, it also took a long time to make progress because it is a hard problem. Thanks to work by Skordis & Zlosnik on a theory they [now] call AeST⁸, it is possible to fit the acoustic power spectrum of the CMB:

This fit is indistinguishable from that of LCDM.

I consider this to be a demonstration, not necessarily the last word on the correct theory, but hopefully an iteration towards one. The point here is that it is possible to fit the CMB. That’s all that matters for our current discussion: contrary to the steady insistence of cosmologists over the past 15 years, CDM is not the only way to fit the CMB. There may be other possibilities that we have yet to figure out. Perhaps even a plurality of possibilities. This is hard work and to make progress we need a critical mass of people contributing to the effort, not shouting rubbish from the peanut gallery.

As I’ve done before, I like to take the language used in favor of dark matter, and see if it also fits when I put on a MOND hat:

As a galaxy dynamicist, let me just remind everyone that the primary reason to believe in MOND as a physical theory and not some curious dark matter phenomenology is the very high precision with which MOND predicts, a priori, the dynamics of low-acceleration systems, especially low surface brightness galaxies whose kinematics were practically unknown at the time of its inception. There is a stone-cold, quantitative, crystal clear prediction of MOND that the kinematics of galaxies follows uniquely from their observed baryon distributions. This is something CDM profoundly and irremediably gets wrong: it predicts that the dark matter halo should have a central cusp⁹ that is not observed, and makes no prediction at all for the baryon distribution, let alone does it account for the detailed correspondence between bumps and wiggles in the baryon distribution and those in rotation curves. This is observed over and over again in hundreds upon hundreds of galaxies, each of which has its own unique mass distribution so that each and every individual case provides a distinct, independent test of the hypothesized force law. In contrast, CDM does not even attempt a comparable prediction: rather than enabling the real-world application to predict that this specific galaxy will have this particular rotation curve, it can only refer to the statistical properties of galaxy-like objects formed in numerical simulations that resemble real galaxies only in the abstract, and can never be used to directly predict the kinematics of a real galaxy in advance of the observation – an ability that has been demonstrated repeatedly by MOND. The simple fact that the simple formula of MOND is so repeatably correct in mapping what we see to what we get is to me the most convincing way to see that we need a grander theory that contains MOND and exactly MOND in the low acceleration limit, irrespective of the physical mechanism by which this is achieved.

That is stronger language than I would ordinarily permit myself. I do so entirely to show the danger of being so darn sure. I actually agree with clayton’s perspective in his quote; I’m just showing what it looks like if we adopt the same attitude with a different perspective. The problems pointed out for each theory are genuine, and the supposed solutions are not obviously viable (in either case). Sometimes I feel like we’re up the proverbial creek without a paddle. I do not know what the right answer is, and you should be skeptical of anyone who is sure that he does. Being sure is the sure road to stagnation.

¹It may surprise some advocates of dark matter that I barely touch on MOND in this course, only getting to it at the end of the semester, if at all. It really is evidence-based, with a focus on the dynamical evidence as there is a lot more to this than seems to be appreciated by most physicists*. We also teach a course on cosmology, where students get the material that physicists seem to be more familiar with.

*I once had a colleague who was is a physics department ask how to deal with opposition to developing a course on galaxy dynamics. Apparently, some of the physicists there thought it was not a rigorous subject worthy of an entire semester course – an attitude that is all too common. I suggested that she pointedly drop the textbook of Binney & Tremaine on their desks. She reported back that this technique proved effective.

²I do not know who clayton is; that screen name does not suffice as an identifier. He claims to have been in contact with me at some point, which is certainly possible: I talk to a lot of people about these issues. He is welcome to contact me again, though he may wish to consider opening with an apology.

³One of the hardest realizations I ever had as a scientist was that both of the reasons (1) and (2) that I believed to absolutely require CDM assumed that gravity was normal. If one drops that assumption, as one must to contemplate MOND, then these reasons don’t require CDM so much as they highlight that something is very wrong with the universe. That something could be MOND instead of CDM, both of which are in the category of who ordered that?

⁴In the early days (late ’90s) when I first started asking why MOND gets any predictions right, one of the people I asked was Joe Silk. He dismissed the rotation curve fits of MOND as a fluke. There were 80 galaxies that had been fit at the time, which seemed like a lot of flukes. I mention this because one of the persistent myths of the subject is that MOND is somehow guaranteed to magically fit rotation curves. Erwin de Blok and I explicitly showed that this was not true in a 1998 paper.

⁵I sometimes hear cosmologists speak in awe of the thousands of observed CMB modes that are fit by half a dozen LCDM parameters. This is impressive, but we’re fitting a damped and driven oscillation – those thousands of modes are not all physically independent. Moreover, as can be seen in the figure from Dodelson & Hu, some free parameters provide more flexibility than others: there is plenty of flexibility in a model with dark matter to fit the CMB data. Only with the Planck data do minor tensions arise, the reaction to which is generally to add more free parameters, like decoupling the primordial helium abundance from that of deuterium, which is anathema to standard BBN so is sometimes portrayed as exciting, potentially new physics.

For some reason, I never hear the same people speak in equal awe of the hundreds of galaxy rotation curves that can be fit by MOND with a universal acceleration scale and a single physical free parameter, the mass-to-light ratio. Such fits are over-constrained, and every single galaxy is an independent test. Indeed, MOND can predict rotation curves parameter-free in cases where gas dominates so that the stellar mass-to-light ratio is irrelevant.

How should we weigh the relative merit of these very different lines of evidence?

⁶On a number of memorable occasions, people shouted “No you didn’t!” On smaller number of those occasions (exactly two), they bothered to look up the prediction in the literature and then wrote to apologize and agree that I had indeed predicted that.

⁷If you read this paper, part of what you will see is me being confused about how low surface brightness galaxies could adhere so tightly to the Tully-Fisher relation. They should not. In retrospect, one can see that this was a MOND prediction coming true, but at the time I didn’t know about that; all I could see was that the result made no sense in the conventional dark matter picture.

Some while after we published that paper, Bob Sanders, who was at the same institute as my collaborators, related to me that Milgrom had written to him and asked “Do you know these guys?”

⁸Initially they had called it RelMOND, or just RMOND. AeST stands for Aether-Scalar-Tensor, and is clearly a step along the lines that Bekenstein made with TeVeS.

In addition to fitting the CMB, AeST retains the virtues of TeVeS in terms of providing a lensing signal consistent with the kinematics. However, it is not obvious that it works in detail – Tobias Mistele has a brand new paper testing it, and it doesn’t look good at extremely low accelerations. With that caveat, it significantly outperforms extant dark matter models.

There is an oft-repeated fallacy that comes up any time a MOND-related theory has a problem: “MOND doesn’t work therefore it has to be dark matter.” This only ever seems to hold when you don’t bother to check what dark matter predicts. In this case, we should but don’t detect the edge of dark matter halos at higher accelerations than where AeST runs into trouble.

⁹Another question I’ve posed for over a quarter century now is what would falsify CDM? The first person to give a straight answer to this question was Simon White, who said that cusps in dark matter halos were an ironclad prediction; they had to be there. Many years later, it is clear that they are not, but does anyone still believe this is an ironclad prediction? If it is, then CDM is already falsified. If it is not, then what would be? It seems like the paradigm can fit any surprising result, no matter how unlikely a priori. This is not a strength, it is a weakness. We can, and do, add epicycle upon epicycle to save the phenomenon. This has been my concern for CDM for a long time now: not that it gets some predictions wrong, but that it can apparently never get a prediction so wrong that we can’t patch it up, so we can never come to doubt it if it happens to be wrong.

Triton Station

A Blog About the Science and Sociology of Cosmology and Dark Matter

Category: particle physics