This clickbait title is inspired by the clickbait title of a recent story about high redshift galaxies observed by JWST. To speak in the same vernacular:
This story is one variation on the work of Labbe et al. that has been making the rounds since it appeared in Nature in late February. The concern is that these high redshift galaxies are big and bright. They got too big too soon.
Six high redshift galaxies from the JWST CEERS survey, as reported by Labbe et al. (2023). Not much to look at, but bear in mind that these objects are pushing the edge of the observable universe. By that standard, they are both bright and disarmingly obvious.
Stellar masses and redshifts of galaxies from Labbe et al. The pink squares are the initial estimates that appeared in their first preprint in July 2022. The black squares with error bars are from the version published in February 2023. The shaded regions represent where galaxies are too massive too early for LCDM. The lighter region is where very few galaxies were expectedto exist; the darker region is a hard no.
The results here are mixed. On the one hand, we were right to be concerned about the initial analysis. This was based in part on a ground-based calibration of the telescope before it was launched. That’s not the same as performance on the sky, which is usually a bit worse than in the lab. JWST breaks that mold, as it is actually performing better than expected. That means the bright-looking galaxies aren’t quite as intrinsically bright as was initially thought.
The correct calibration reduces both the masses and the redshifts of these galaxies. The change isn’t subtle: galaxies are less massive (the mass scale is logarithmic!) and at lower redshift than initially thought. Amusingly, only one galaxy is above redshift 9 when the early talking point was big galaxies at z = 10. (There are othercrediblecandidates for that.) Nevertheless, the objects are clearly there, and bright (i.e., massive). They are also early. We like to obsess about redshift, but there is an inverse relation between redshift and time, so there is not much difference in clock time between z = 7 and 10. Redshift 10 is just under 500 million years after the big bang; redshift 7 just under 750 million years. Those are both in the first billion years out of a current age of over thirteen billion years. The universe was still in its infancy for both.
Regardless of your perspective on cosmic time scales, the observed galaxies remain well into LCDM’s danger zone, even with the revised calibration. They are no longer fully in the no-go zone, so I’m sure we’ll see lots of papers explaining how the danger zone isn’t so dangerous after all, and that we should have expected it all along. That’s why it matters more what we predict before an observation than after the answer is known.
*I emphasize science here because one of the reactions I get when I point out that this was predicted is some variation on “That doesn’t count! [because I don’t understand the way it was done.]” And yet, the predictions made and published in advance of the observations keep coming true. It’s almost as if there might be something to this so-called scientific method.
On the one hand, I understand the visceral negative reaction. It is the same reaction I had when MOND first reared its ugly head in my own data for low surface brightness galaxies. This is apparently a psychological phasethrough which we must pass. On the other hand, the community seems stuck in this rut: it is high time to get past it. I’ve been trying to educate a reluctant audience for over a quarter century now. I know how it pains them because I shared that pain. I got over it. If you’re a scientist still struggling to do so, that’s on you.
There are some things we have to figure out for ourselves. If you don’t believe me, fine, but then get on with doing it yourself instead of burying your head in the sand. The first thing you have to do is give MOND a chance. When I allowed that possibility, I suddenly found myself working less hard than when I was desperately trying to save dark matter. If you come to the problem sure MOND is wrong+, you’ll always get the answer you want.
+I’ve been meaning to write a post (again) about the very real problems MOND suffers in clusters of galaxies. This is an important concern. It is also just one of hundreds of things to consider in the balance. We seem willing to give LCDM infinite mulligans while any problem MOND encounters is immediately seen as fatal. If we hold them to the same standard, both are falsified. If all we care about is explanatory power, LCDM always has that covered. If we care more about successful a priori predictions, MOND is less falsified than LCDM.
There is an important debate to be had on these issues, but we’re not having it. Instead, I frequently encounter people whose first response to any mention of MOND is to cite the bullet cluster in order to shut down discussion. They are unwilling to accept that there is a debate to be had, and are inevitably surprised to learn that LCDM has trouble explaining the bullet cluster too, let alone other clusters. It’s almost as if they are just looking for an excuse to not have to engage in serious thought that might challenge their belief system.
I want to start by thanking those of you who have contributed to maintaining this site. This is not a money making venture, but it does help offset the cost of operations.
The title is not related to this, but rather to a flood of papers addressing the questions posed in recent posts. I was asking last time “take it where?” because it is hard to know what cosmology under UT will look like. In particular, how does structure formation work? We need a relativistic theory to progress further than we already have.
There are some papers that partially address this question. Very recently, there have been a whole slew of them. That’s good! It is also a bit overwhelming – I cannot keep up! Here I note a few recent papers that touch on structure formation in MOND. This is an incomplete list, and I haven’t had the opportunity to absorb much of it.
First, there is a paper by Milgrom with his relativistic BIMOND theory. It shows some possibility of subtle departures from FLRW along the lines of what I was describing with UT. Intriguingly, it explicitly shows that the assumptions we made to address structure formation with plain MOND should indeed hold. This is important because a frequent excuse employed to avoid acknowledging MOND’s predictions is that they don’t count if there is no relativistic theory. This is more a form of solution aversion rather than a serious scientific complaint, but people sure lean hard into it. So go read Milgrom’s papers.
Another paper I was looking forward to but didn’t know was in the offing is a rather general treatment of structure formation in relativistic extensions of MOND. There does seem to be some promise for assessing what could work in theories like AeST, and how it relates to earlier work. As a general treatment, there are a lot of options to sort through. Doing so will take a lot of effort by a lot of people over a considerable span of time.
There is also work on gravitational waves, and a variation dubbed a khronometric theory. I, well, I know what both of them are talking about to some extent, and yet some of what they say is presently incomprehensible to me. Clearly I have a lot still to learn. That’s a good problem to have.
I have been thinking for a while now that what we need is a period of a theoretical wild west. People need to try ideas, work through their consequences, and see what works and what does not. Ultimately, most ideas will fail, as there can only be one correct depiction of reality (I sure hope). It will take a lot of work and angst and bickering before we get there: this is perhaps only the beginning of what has already been a long journey for those of us who have been paying attention.
New and stirring things are belittled because if they are not belittled, the humiliating question arises, ‘Why then are you not taking part in them?’
I had written most of the post below the line before an exchange with a senior colleague who accused me of asking us to abandon General Relativity (GR). Anyone who read the last post knows that this is the opposite of true. So how does this happen?
Much of the field is mired in bad ideas that seemed like good ideas in the 1980s. There has been some progress, but the idea that MOND is an abandonment of GR I recognize as a misconception from that time. It arose because the initial MOND hypothesis suggested modifying the law of inertia without showing a clear path to how this might be consistent with GR. GR was built on the Equivalence Principle (EP), the equivalence1 of gravitational charge with inertial mass. The original MOND hypothesis directly contradicted that, so it was a fair concern in 1983. It was not by 19842. I was still an undergraduate then, so I don’t know the sociology, but I get the impression that most of the community wrote MOND off at this point and never gave it further thought.
I guess this is why I still encounter people with this attitude, that someone is trying to rob them of GR. It’s feels like we’re always starting at square one, like there has been zero progress in forty years. I hope it isn’t that bad, but I admit my patience is wearing thin.
I’m trying to help you. Don’t waste you’re entire career chasing phantoms.
What MOND does ask us to abandon is the Strong Equivalence Principle. Not the Weak EP, nor even the Einstein EP. Just the Strong EP. That’s a much more limited ask that abandoning all of GR. Indeed, all flavors of EP are subject to experimental test. The Weak EP has been repeatedly validated, but there is nothing about MOND that implies platinum would fall differently from titanium. Experimental tests of the Strong EP are less favorable.
I understand that MOND seems impossible. It also keeps having its predictions come true. This combination is what makes it important. The history of science is chock full of ideas that were initially rejected as impossible or absurd, going all the way back to heliocentrism. The greater the cognitive dissonance, the more important the result.
Continuing the previous discussion of UT, where do we go from here? If we accept that maybe we have all these problems in cosmology because we’re piling on auxiliary hypotheses to continue to be able to approximate UT with FLRW, what now?
I don’t know.
It’s hard to accept that we don’t understand something we thought we understood. Scientists hate revisiting issues that seem settled. Feels like a waste of time. It also feels like a waste of time continuing to add epicycles to a zombie theory, be it LCDM or MOND or the phoenix universe or tired light or whatever fantasy reality you favor. So, painful as it may be, one has find a little humility to step back and take account of what we know empirically independent of the interpretive veneer of theory.
Still, to give one pertinent example, BBN only works if the expansion rate is as expected during the epoch of radiation domination. So whatever is going on has to converge to that early on. This is hardly surprising for UT since it was stipulated to contain GR in the relevant limit, but we don’t actually know how it does so until we work out what UT is – a tall order that we can’t expect to accomplish overnight, or even over the course of many decades without a critical mass of scientists thinking about it (and not being vilified by other scientists for doing so).
Another example is that the cosmological principle – that the universe is homogeneous and isotropic – is observed to be true in the CMB. The temperature is the same all over the sky to one part in 100,000. That’s isotropy. The temperature is tightly coupled to the density, so if the temperature is the same everywhere, so is the density. That’s homogeneity. So both of the assumptions made by the cosmological principle are corroborated by observations of the CMB.
The cosmological principle is extremely useful for solving the equations of GR as applied to the whole universe. If the universe has a uniform density on average, then the solution is straightforward (though it is rather tedious to work through to the Friedmann equation). If the universe is not homogeneous and isotropic, then it becomes a nightmare to solve the equations. One needs to know where everything was for all of time.
Starting from the uniform condition of the CMB, it is straightforward to show that the assumption of homogeneity and isotropy should persist on large scales up to the present day. “Small” things like galaxies go nonlinear and collapse, but huge volumes containing billions of galaxies should remain in the linear regime and these small-scale variations average out. One cubic Gigaparsec will have the same average density as the next as the next, so the cosmological principle continues to hold today.
Anyone spot the rub? I said homogeneity and isotropy should persist. This statement assumes GR. Perhaps it doesn’t hold in UT?
This aspect of cosmology is so deeply embedded in everything that we do in the field that it was only recently that I realized it might not hold absolutely – and I’ve been actively contemplating such a possibility for a long time. Shouldn’t have taken me so long. Felten (1984) realized right away that a MONDian universe would depart from isotropy by late times. I read that paper long ago but didn’t grasp the significance of that statement. I did absorb that in the absence of a cosmological constant (which no one believed in at the time), the universe would inevitably recollapse, regardless of what the density was. This seems like an elegant solution to the flatness/coincidence problem that obsessed cosmologists at the time. There is no special value of the mass density that provides an over/under line demarcating eternal expansion from eventual recollapse, so there is no coincidence problem. All naive MOND cosmologies share the same ultimate fate, so it doesn’t matter what we observe for the mass density.
MOND departs from isotropy for the same reason it forms structure fast: it is inherently non-linear. As well as predicting that big galaxies would form by z=10, Sanders (1998) correctly anticipated the size of the largest structures collapsing today (things like the local supercluster Laniakea) and the scale of homogeneity (a few hundred Mpc if there is a cosmological constant). Pretty much everyone who looked into it came to similar conclusions.
But MOND and cosmology, as we know it in the absence of UT, are incompatible. Where LCDM encompasses both cosmology and the dynamics of bound systems (dark matter halos3), MOND addresses the dynamics of low acceleration systems (the most common examples being individual galaxies) but says nothing about cosmology. So how do we proceed?
For starters, we have to admit our ignorance. From there, one has to assume some expanding background – that much is well established – and ask what happens to particles responding to a MONDian force-law in this background, starting from the very nearly uniform initial condition indicated by the CMB. From that simple starting point, it turns out one can get a long way without knowing the details of the cosmic expansion history or the metric that so obsess cosmologists. These are interesting things, to be sure, but they are aspects of UT we don’t know and can manage without to some finite extent.
For one, the thermal history of the universe is pretty much the same with or without dark matter, with or without a cosmological constant. Without dark matter, structure can’t get going until after thermal decoupling (when the matter is free to diverge thermally from the temperature of the background radiation). After that happens, around z = 200, the baryons suddenly find themselves in the low acceleration regime, newly free to respond to the nonlinear force of MOND, and structure starts forming fast, with the consequences previously elaborated.
But what about the expansion history? The geometry? The big questions of cosmology?
Again, I don’t know. MOND is a dynamical theory that extends Newton. It doesn’t address these questions. Hence the need for UT.
I’ve encountered people who refuse to acknowledge4 that MOND gets predictions like z=10 galaxies right without a proper theory for cosmology. That attitude puts the cart before the horse. One doesn’t look for UT unless well motivated. That one is able to correctly predict 25 years in advance something that comes as a huge surprise to cosmologists today is the motivation. Indeed, the degree of surprise and the longevity of the prediction amplify the motivation: if this doesn’t get your attention, what possibly could?
There is no guarantee that our first attempt at UT (or our second or third or fourth) will work out. It is possible that in the search for UT, one comes up with a theory that fails to do what was successfully predicted by the more primitive theory. That just lets you know you’ve taken a wrong turn. It does not mean that a correct UT doesn’t exist, or that the initial prediction was some impossible fluke.
One candidate theory for UT is bimetric MOND. This appears to justify the assumptions made by Sanders’s early work, and provide a basis for a relativistic theory that leads to rapid structure formation. Whether it can also fit the acoustic power spectrum of the CMB as well as LCDM and AeST has yet to be seen. These things take time and effort. What they really need is a critical mass of people working on the problem – a community that enjoys the support of other scientists and funding institutions like NSF. Until we have that5, progress will remain grudgingly slow.
1The equivalence of gravitational charge and inertial mass means that the m in F=GMm/d2 is identically the same as the m in F=ma. Modified gravity changes the former; modified inertia the latter.
2Bekenstein & Milgrom (1984) showed how a modification of Newtonian gravity could avoid the non-conservation issues suffered by the original hypothesis of modified inertia. They also outlined a path towards a generally covariant theory that Bekenstein pursued for the rest of his life. That he never managed to obtain a completely satisfactory version is often cited as evidence that it can’t be done, since he was widely acknowledged as one of the smartest people in the field. One wonders why he persisted if, as these detractors would have us believe, the smart thing to do was not even try.
4I have entirely lost patience with this attitude. If a phenomena is correctly predicted in advance in the literature, we are obliged as scientists to take it seriously+. Pretending that it is not meaningful in the absence of UT is just an avoidance strategy: an excuse to ignore inconvenient facts.
+I’ve heard eminent scientists describe MOND’s predictive ability as “magic.” This also seems like an avoidance strategy. I, for one, do not believe in magic. That it works as well as it does – that it works at all – must be telling us something about the natural world, not the supernatural.
5There does exist a large and active community of astroparticle physicists trying to come up with theories for what the dark matter could be. That’s good: that’s what needs to happen, and we should exhaust all possibilities. We should do the same for new dynamical theories.
Imagine if you are able that General Relativity (GR) is correct yet incomplete. Just as GR contains Newtonian gravity in the appropriate limit, imagine that GR itself is a limit of some still more general theory that we don’t yet know about. Let’s call it Underlying Theory (UT) for short. This is essentially the working hypothesis of quantum gravity, but here I want to consider a more general case in which the effects of UT are not limited to the tiny netherworld of the Planck scale. Perhaps UT has observable consequences on very large scales, or a scale that is not length-based at all. What would that look like, given that we only know GR?
For starters, it might mean that the conventional Friedmann-Robertson-Walker (FRW) cosmology derived from GR is only a first approximation to the cosmology of the unknown deeper theory UT. In the first observational tests, FRW will look great, as the two are practically indistinguishable. As the data improve though, awkward problems might begin to crop up. What and where we don’t know, so our first inclination will not be to infer the existence of UT, but rather to patch up FRW with auxiliary hypotheses. Since the working presumption here is that GR is a correct limit, FRW will continue be a good approximation, and early departures will seem modest: they would not be interpreted as signs of UT.
What do we expect for cosmology anyway? A theory is only as good as its stated predictions. After Hubble established in the 1920s that galaxies external to the Milky Way existed and that the universe was expanding, it became clear that this was entirely natural in GR. Indeed, what was not natural was a static universe, the desire for which had led Einstein to introduce the cosmological constant (his “greatest blunder”).
A wide variety of geometries and expansion histories are possible with FRW. But there is one obvious case that stands out, that of Einstein-de Sitter (EdS, 1932). EdS has a matter density Ωm exactly equal to unity, balancing on the divide between a universe that expands forever (Ωm < 1) and one that eventually recollapses (Ωm > 1). The particular case Ωm = 1 is the only natural scale in the theory. It is also the only FRW model with a flat geometry, in the sense that initially parallel beams of light remain parallel indefinitely. These properties make it special in a way that obsessed cosmologists for many decades. (In retrospect, this obsession has the same flavor as the obsession the Ancients had with heavenly motions being perfect circles*.) A natural cosmology would therefor be one in which Ωm = 1 in normal matter (baryons).
By the 1970s, it was clear that there was no way you could have Ωm = 1 in baryons. There just wasn’t enough normal matter, either observed directly, or allowed by Big Bang Nucleosynthesis. Despite the appeal of Ωm = 1, it looked like we lived in an open universe with Ωm < 1.
This did not sit well with many theorists, who obsessed with the flatness problem. The mass density parameter evolves if it is not identically equal to one, so it was really strange that we should live anywhere close to Ωm = 1, even Ωm = 0.1, if the universe was going to spend eternity asymptoting to Ωm → 0. It was a compelling argument, enough to make most of us accept (in the early 1980s) the Inflationary model of the early universe, as Inflation gives a natural mechanism to drive Ωm → 1. The bulk of this mass could not be normal matter, but by then flat rotation curves had been discovered, along with a ton of other evidence that a lot of matter was dark. A third element that came in around the same time was another compelling idea, supersymmetry, which gave a natural mechanism by which the unseen mass could be non-baryonic. The confluence of these revelations gave us the standard cold dark matter (SCDM) cosmological model. It was EdS with Ωm = 1 mostly in dark matter. We didn’t know what the dark matter was, but we had a good idea (WIMPs), and it just seemed like a matter of tracking them down.
SCDM was absolutely Known for about a decade, pushing two depending on how you count. We were very reluctant to give it up. But over the course of the 1990s, it became clear [again] that Ωm < 1. What was different was a willingness, even a desperation, to accept and rehabilitate Einstein’s cosmological constant. This seemed to solve all cosmological problems, providing a viable concordance cosmology that satisfied all then-available data, salvaged Inflation and a flat geometry (Ωm + ΩΛ = 1, albeit at the expense of the coincidence problem, which is worse in LCDM than it is in open models), and made predictions that came true for the accelerated expansion rate and the location of the first peak of the acoustic power spectrum. This was a major revelation that led to Nobel prizes and still resonates today in the form of papers trying to suss out the nature of this so-called dark energy.
What if the issue is even more fundamental? Taking a long view, subsuming many essentialdetails, we’ve gone from a natural cosmology (EdS) to a less natural one (an open universe with a low density in baryons) to SCDM (EdS with lots of non-baryonic dark matter) to LCDM. Maybe these are just successive approximations we’ve been obliged to make in order for FLRW** to mimic UT? How would we know?
One clue might be if the concordance region closed. Here is a comparison of a compilation of constraints assembled by students in my graduate cosmology course in 2002 (plus 2003 WMAP) with 2018 Planck parameters:
The shaded regions were excluded by the sum of the data available in 2003. The question I wondered then was whether the small remaining white space was indeed the correct answer, or merely the least improbable region left before the whole picture was ruled out. Had we painted ourselves into a corner?
If we take these results and the more recent Planck fits at face value, yes: nothing is left, the window has closed. However, other things change over time as well. For example, I’d grant a higher upper limit to Ωm than is illustrated above. The rotation curve line represents an upper limit that no longer pertains if dark matter halos are greatly modified by feedback. We were trying to avoid invoking that deus ex machina then, but there’s no helping it now.
Still, you can see in this diagram what we now call the Hubble tension. To solve that within the conventional FLRW framework, we have to come up with some new free parameter. There are lots of ideas that invoke new physics.
Maybe the new physics is UT? Maybe we have to keep tweaking FLRW because cosmology has reached a precision such that FLRW is no longer completely adequate as an approximation to UT? But if we are willing to add new parameters via “new physics” made up to address each new problem (dark matter, dark energy, something new and extra for the Hubble tension) so we can keep tweaking it indefinitely, how would we ever recognize that all we’re doing is approximating UT? If only there were different data that suggested new physics in an independent way.
Attitude matters. If we think both LCDM and the existence of dark matter is proven beyond a reasonable doubt, as clearlymany physicists do, then any problem that arises is just a bit of trivia to sort out. Despite the current attention being given to the Hubble tension, I’d wager that most of the people not writing papers about it are presuming that the problem will go away: traditional measures of the Hubble constant will converge towards the Planck value. That might happen (or appear to happen through the magic of confirmation bias), and I would expect that myself if I hadn’t worked on H0 directly. It’s a lot easier to dismiss such things when you haven’t been involved enough to know how hard they are to dismiss***.
That last sentence pretty much sums up the community’s attitude towards MOND. That led me to pose the question of the year earlier. I have not heard any answers, just excuses to not have to answer. Still, these issues are presumably not unrelated. That MOND has so many predictions – even in cosmology – come true is itself an indication of UT. From that perspective, it is not surprising that we have to keep tweaking FLRW. Indeed, from this perspective, parameters like ΩCDM are chimeras lacking in physical meaning. They’re just whatever they need to be to fit whatever subset of the data is under consideration. That independent observations pretty much point to the same value is far compelling evidence in favor of LCDM than the accuracy of a fit to any single piece of information (like the CMB) where ΩCDM can be tuned to fit pretty much any plausible power spectrum. But is the stuff real? I make no apologies for holding science to a higher standard than those who consider a fit to the CMB data to be a detection.
It has taken a long time for cosmology to get this far. One should take a comparably long view of these developments, but we generally do not. Dark matter was already received wisdom when I was new to the field, unquestionably so. Dark energy was new in the ’90s but has long since been established as received wisdom. So if we now have to tweak it a little to fix this seemingly tiny tension in the Hubble constant, that seems incremental, not threatening to the pre-existing received wisdom. From the longer view, it looks like just another derailment in an excruciatingly slow-moving train wreck.
So I ask again: what would falsify FLRW cosmology? How do we know when to think outside this box, and not just garnish its edges?
*The obsession with circular motion continued through Copernicus, who placed the sun at the center of motion rather than the earth, but continued to employ epicycles. It wasn’t until over a half century later that Kepler finally broke with this particular obsession. In retrospect, we recognize circular motion as a very special case of the many possibilities available with elliptical orbits, just as EdS is only one possible cosmology with a flat geometry once we admit the possibility of a cosmological constant.
**FLRW = Friedmann-Lemaître-Robertson-Walker. I intentionally excluded Lemaître from the early historical discussion because he (and the cosmological constant) were mostly excluded from considerations at that time. Mostly.
Someone with a longer memory than my own is Jim Peebles. I happened to bump into him while walking across campus while in Princeton for a meeting in early 2019. (He was finally awarded a Nobel prize later that year; it should have been in association with the original discovery of the CMB). On that occasion, he (unprompted) noted an analogy between the negative attitude towards the cosmological constant that was prevalent in the community pre-1990s to that for MOND now. NOT that he was in any way endorsing MOND; he was just noting that the sociology had the same texture, and could conceivably change on a similar timescale.
***Note that I am not dismissing the Planck results or any other data; I am suggesting the opposite: the data have become so good that it is impossible to continue to approximate UT with tweaks to FLRW (hence “new physics”). I’m additionally pointing out that important new physics has been staring us in the face for a long time.
Cosmology is challenged at present by two apparently unrelated problems: the apparent formation of large galaxies at unexpectedly high redshift observed by JWST, and the tension between the value of the Hubble constant obtained by traditional methods and that found in multi-parameter fits to the acoustic power spectrum of the cosmic microwave background (CMB).
Early results in precision cosmology from WMAP obtained estimates of the Hubble constant h = 0.73 ± 0.03 [I adopt the convention h = H0/(100 km s-1 Mpc-1) so as not to have to have to write the units every time.] This was in good agreement with contemporaneous local estimates from the Hubble Space Telescope Key Project to Measure the Hubble Constant: h = 0.72 ± 0.08. This is what Hubble was built to do. It did it, and the vast majority of us were satisfied* at the time that it had succeeded in doing so.
Since that time, a tension has emerged as accuracy has improved. Precise local measures** give h = 0.73 ± 0.01 while fits to the Planck CMB data give h = 0.6736 ± 0.0054. This is around the 5 sigma threshold for believing there is a real difference. Our own results exclude h < 0.705 at 95% confidence. A value as low as 67 is right out.
Given the history of the distance scale, it is tempting to suppose that local measures are at fault. This seems to be the prevailing presumption, and it is just a matter of figuring out what went wrong this time. Of course, things can go wrong with the CMB too, so this way of thinking raises the ever-present danger of confirmation bias, ever a scourge in cosmology. Looking at the history of H0 determinations, it is not local estimates of H0 but rather those from CMB fits that have diverged from the concordance region.
The cosmic mass density parameter and Hubble constant. These covary in CMB fits along the line Ωmh3 = 0.09633 ± 0.00029 (red). Also shown are best-fit values from CMB experiments over time, as labeled (WMAP3 is the earliest shown; Planck2018 the most recent). These all fall along the line of constant Ωmh3, but have diverged over time from concordance with local data. There are many examples of local constraints; for illustration I show examples from Cole et al. (2005), Mohayaee & Tully (2005), Tully et al. (2016), and Riess et al. (2001). The divergence has occurred as finer angular scales have been observed in the CMB power spectrum and correspondingly higher multiples ℓ have been incorporated into fits.
The divergence between local and CMB-determined H0 has occurred as finer angular scales have been observed in the CMB power spectrum and correspondingly higher multiples ℓ have been incorporated into fits. That suggests that the issue resides in the high-ℓ part of the CMB data*** rather than in some systematic in the local determinations. Indeed, if one restricts the analysis of the Planck (“TT”) data to ℓ < 801, one obtains h = 0.70 ± 0.02 (see their Fig. 22), consistent with earlier CMB estimates as well as with local ones.
Photons must traverse the entire universe to reach us from the surface of last scattering. Along the way, they are subject to 21 cm absorption by neutral hydrogen, Thomson scattering by free electrons after reionization, blue and redshifting from traversing gravitational potentials in an expanding universe (the late ISW effect, aka the Rees-Sciama effect), and deflection by gravitational lensing. Lensing is a subtle effect that blurs the surface of last scattering and adds a source of fluctuations not intrinsic to it. The amount of lensing can be calculated from the growth rate of structure; anomalously fast galaxy formation would induce extra power at high ℓ.
Early Galaxy Formation
JWST observations evince the early emergence of massive galaxies at z ≈ 10. This came as a great surprise theoretically, but the empirical result extends previous observations that galaxies grew too bigtoo fast. Taking the data at face value, more structure appears to exist in the early universe than anticipated in the standard calculation. This would cause excess lensing and an anomalous source of power on fine scales. This would be a real, physical anomaly (new physics), not some mistake in the processing of CMB data (which may of course happen, just as with any other sort of data). Here are the Planck data:
Unbinned Planck data with the best-fit power spectrum (red line) and a model (blue line) with h=0.73 and Ωm adjusted to maintain constant Ωmh3. The ratio of the models is shown at bottom, that with = 0.67 divided by the model with h = 0.73. The difference is real; h = 0.67 gives the better fit****. The ratio illustrates the subtle need for slightly greater power with increasing ℓ than provided by the model with h = 0.73. Perhaps this high-ℓ power has a contribution from anomalous gravitational lensing that skews the fit and drives the Hubble tension.
If excess lensing by early massive galaxies occurs but goes unrecognized, fits to the CMB data would be subtly skewed. There would be more power at high ℓ than there should be. Fitting this extra power would drive up Ωm and other relevant parameters*****. In response, it would be necessary to reduce h to maintain a constant Ωmh3. This would explain the temporal evolution of the best fit values, so I posit that this effect may be driving the Hubble tension.
The early formation of massive galaxies would represent a real, physical anomaly. This is unexpected in ΛCDM but not unanticipated. Sanders (1998) explicitly predicted the formation of massive galaxies by z = 10. Excess gravitational lensing by these early galaxies is a natural consequence of his prediction. Other things follow as well: early reionization, an enhanced ISW/Rees-Sciama effect, and high redshift21 cm absorption. In short, everything that is puzzling about the early universe from the ΛCDM perspective was anticipated and often explicitly predicted in advance.
The new physics driving the prediction of Sanders (1998) is MOND. This is the same driver of anomalies in galaxy dynamics, and perhaps now also of the Hubble tension. These predictive successes must be telling us something, and highlight the need for a deeper theory. Whether this finally breaks ΛCDM or we find yet another unsatisfactory out is up to others to decide.
*Indeed, the ± 0.08 rather undersells the accuracy of the result. I quote that because the Key Project team gave it as their bottom line. However, if you read the paper, you see statements like h = 0.71 ± 0.02 (random) ± 0.06 (systematic). The first is the statistical error of the experiment, while the latter is an estimate of how badly it might go wrong (e.g., susceptibility to a recalibration of the Cepheid scale). With the benefit of hindsight, we can say now that the Cepheid calibration has not changed that much: they did indeed get it right to something more like ± 0.02 than ± 0.08.
***I recall being at a conference when the Planck data were fresh where people were visibly puzzled at the divergence of their fit from the local concordance region. It was obvious to everyone that this had come about when the high ℓ data were incorporated. We had no idea why, and people were reluctant to contradict the Authority of the CMB fit, but it didn’t sit right. Since that time, the Planck result has been normalized to the point where I hear its specific determination of cosmic parameters used interchangeably with ΛCDM. And indeed, the best fit is best for good reason; determinations that are in conflict with Planck are either wrong or indicate new physics.
****The sharp eye will also notice a slight offset in the absolute scale. This is fungible with the optical depth due to reionization, which acts as a light fog covering the whole sky: higher optical depth τ depresses the observed amplitude of the CMB. The need to fit the absolute scale as well as the tip in the shape of the power spectrum would explain another temporal evolution in the best-fit CMB parameters, that of declining optical depth from WMAP and early (2013) Planck (τ = 0.09) to 2018 Planck (τ = 0.0544).
*****The amplitude of the power spectrum σ8 would also be affected. Perhaps unsurprisingly, there is also a tension between local and CMB determinations of this parameter. All parameters must be fit simultaneously, so how it comes out in the wash depends on the details of the history of the nonlinear growth of structure. Such a calculation is beyond the scope of this note. Indeed, I hope someone else takes up the challenge, as I tire of solving all the problems only to have them ignored. Better if everyone else comes to grip with this for themselves.
Something that Sabine Hossenfelder noted recently on Twitter resonated with me:
This is a very real problem in academia, and I don’t doubt that it is a common feature of many human endeavors. Part of it is just that people don’t know enough to know what they don’t know. That is to say, so much has been written that it can be hard to find the right reference to put any given fever dream promptly to never-ending sleep. However, that’s not the real problem.
The problem is exactly what Sabine says it is. People keep pushing ideas that have been debunked. Why let facts get in the way of a fancy idea?
There are lots of examples of this in my own experience. Indeed, I’ve encountered it so often that I’ve concluded that there is no result so obvious that some bozo won’t conclude exactly the opposite.
I spent a lot of my early career working in the context of non-baryonic dark matter. For a long time, I was enthusiastic about it, but I’ve become skeptical. I continue to work on it, just in case. But I soured on it for good reasons, reasons I have explained repeatedly in exhaustive detail. Some people appreciate this level of detail, but most do not. This is the sort of thing Sabine is talking about. People don’t engage seriously with these problems.
Maybe I’m wrong to be skeptical of dark matter? I could accept that – one cannot investigate this wide universe in which we find ourselves without sometimes coming to the wrong conclusions. Has it been demonstrated that the concerns I raised were wrong? No. Rather than grapple with the problems raised, people have simply ignored them – or worse, assert that they aren’t problems at all without demonstrating anything of the sort. Heck, I’ve even seen people take lists of problems and spin them as virtues.
To give one very quick example, consider the physical interpretation of the Tully-Fisher relation. This has varied over time, and there are many flavors. But usually it is supposed that the luminosity is set by the stellar mass, and the rotation speed by the dark matter mass. If we (reasonably) presume that the stellar mass is proportional to the dark mass, viola – Tully-Fisher. This all sounds perfectly plausible, so most people don’t think any harder about it. No problem at al.
Well, one small problem: this explanation does not work. The velocity is not uniquely set by the dark matter halo. In the range of radii accessible to measurement, the contribution of the baryonic mass is non-negligible in high surface brightness galaxies. If that sounds a little technical, it is. One has to cope at this level to play in the sandbox.
Once we appreciate that we cannot just ignore the baryons, explaining Tully-Fisher becomes a lot harder – in particular, the absence of surface brightness residuals. Higher surface brightness galaxies should rotate faster at a given mass, but they don’t. The easy way to fix this is to suppose that the baryonic mass is indeed negligible, but this leads straight to a contradiction with the diversity of rotation curves following from the central density relation. The kinematics know about the shape of the baryonic mass distribution, not just its total. Solving all these problems simultaneously becomes a game of cosmic whack-a-mole: fixing one aspect of the problem makes another worse. All too often, people are so focused on one aspect of a problem that they don’t realize that their fix comes at the expense of something else. It’s like knocking a hole in one side of a boat to obtain material to patch a hole in the other side of the same boat.
Except they are sure. Problem solved! is what people want to hear, so that’s what they hear. Nobody bothers to double check whether the “right” answer in indeed right when it agrees with their preconceptions. And there is always someone willing to make that assertion.
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:
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 Ωm > Ωb 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, A1:2. 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, A2:3. It is, in fact, way off, while LCDM is consistent with A2:3, 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 A2:3, but it had already got A1:2 wrong. We had to adjust the baryon densityoutside 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 A1:2 < 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 Ωbh2 < 0.02, with the consensus value being Ωbh2 = 0.0125 ± 0.0005. This is barely half the value subsequently required to fit the CMB (Ωbh2 = 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: A1:2 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 A2:3. 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.
In those days, when No-CDM was the only correct a priori prediction, I would point out to cosmologists that it had got A1:2 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.
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.
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 A2:3 = 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.
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 whichthereisplenty – 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 Beklenstein‘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:
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 minortensions 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.
That’s the question of the year, and perhaps of the century. I’ve been asking it since before this century began, and I have yet to hear a satisfactory answer. Most of the relevant scientific community has aggressively failed to engage with it. Even if MOND is wrong for [insert favorite reason], this does not relieve us of the burden to understand why it gets many predictions right – predictions that have repeatedly come as a surprise to the community that has declined to engage, preferring to ignore the elephant in the room.
It is not good enough to explain MOND phenomenology post facto with some contrived LCDM model. That’s mostly1 what is on offer, being born of the attitude that we’re sure LCDM is right, so somehow MOND phenomenology must emerge from it. We could just as [un]reasonably adopt the attitude that MOND is correct, so surely LCDM phenomenology happens as a result of trying to fit the standard cosmological model to some deeper, subtly different theory.
A basic tenet of the scientific method is that if a theory has its predictions come true, we are obliged to acknowledge its efficacy. This is how we know when to change our minds. This holds even if we don’t like said theory – especially if we don’t like it.
That was my experience with MOND. It correctly predicted the kinematics of the low surface brightness galaxies I was interested in. Dark matter did not. The data falsified all the models available at the time, including my own dark matter-based hypothesis. The only successful a priori predictions were those made by Milgrom. So what am I to conclude2 from this? That he was wrong?
I understand the reluctance to engage. It really ticked me off that my own model was falsified. How could this stupid theory of Milgrom’s do better for my galaxies? Indeed, how could it get anything right? I had no answer to this, nor does the wider community. It is not for lack of trying on my part; I’ve spent a lot of time3 building conventional dark matter models. They don’t work. Most of the models made by others that I’ve seen are just variations on models I had already considered and rejected as obviously unworkable. They might look workable from one angle, but they inevitably fail from some other, solving one problem at the expense of another.
Predictive success does not guarantee that a theory is right, but it does make it better than competing theories that fail for the same prediction. This is where MOND and LCDM are difficult to compare, as the relevant data are largely incommensurate. Where one is eloquent, the other tends to be muddled. However, it has been my experience that MOND more frequently reproduces the successes of dark matter than vice-versa. I expect this statement comes as a surprise to some, as it certainly did to me (see the comment line of astro-ph/9801102). The people who say the opposite clearly haven’t bothered to check2 as I have, or even to give MOND a real chance. If you come to a problem sure you know the answer, no data will change your mind. Hence:
A challenge: What would falsify the existence of dark matter?
If LCDM is a scientific theory, it should be falsifiable4. Dark matter, by itself, is a concept, not a theory: mass that is invisible. So how can we tell if it’s not there? Once we have convinced ourselves that the universe is full of invisible stuff that we can’t see or (so far) detect any other way, how do we disabuse ourselves of this notion, should it happen to be wrong? If it is correct, we can in principle find it in the lab, so its existence can be confirmed. But is it falsifiable? How?
That is my challenge to the dark matter community: what would convince you that the dark matter picture is wrong? Answers will vary, as it is up to each individual to decide for themself how to answer. But there has to be an answer. To leave this basic question unaddressed is to abandon the scientific method.
I’ll go first. Starting in 1985 when I was first presented evidence in a class taught by Scott Tremaine, I was as much of a believer in dark matter as anyone. I was even a vigorous advocate, for a time. What convinced me to first doubt the dark matter picture was the fine-tuning I had to engage in to salvage it. It was only after that experience that I realized that the problems I was encountering were caused by the data doing what MOND had predicted – something that really shouldn’t happen if dark matter is running the show. But the MOND part came after; I had already become dubious about dark matter in its own context.
Falsifiability is a question every scientist who works on dark matter needs to face. What would cause you to doubt the existence of dark matter? Nothing is not a scientific answer. Neither is it correct to assert that the evidence for dark matter is already overwhelming. That is a misstatement: the evidence for acceleration discrepancies is overwhelming, but these can be interpreted as evidence for either dark matter or MOND.
This important thing is to establish criteria by which you would change your mind. I changed my mind before: I am no longer convinced that the solution the acceleration discrepancy has to be non-baryonic dark matter. I will change my mind again if the evidence warrants. Let me state, yet again, what would cause me to doubt that MOND is a critical element of said solution. There are lots of possibilities, as MOND is readily falsifiable. Three important ones are:
MOND getting a fundamental prediction wrong;
Detecting dark matter;
Answering the question of the year.
None of these have happened yet. Just shouting MOND is falsified already! doesn’t make it so: the evidence has to be both clear and satisfactory. For example,
MOND might be falsified by cluster data, but it’s apparent failure is not fundamental. There is a residual missing mass problem in the richest clusters, but there’s nothing in MOND that says we have to have detected all the baryons by now. Indeed, LCDM doesn’t fare better, just differently, with both theories suffering a missing baryon problem. The chief difference is that we’re willing to give LCDM endless mulligans but MOND none at all. Where the problem for MOND in clusters comes up all the time, the analogous problem in LCDM is barely discussed, and is not even recognized as a problem.
A detection of dark matter would certainly help. To be satisfactory, it can’t be an isolated signal in a lone experiment that no one else can reproduce. If a new particle is detected, its properties have to be correct (e.g, it has the right mass density, etc.). As always, we must be wary of some standard model event masquerading as dark matter. WIMP detectors will soon reach the neutrino background accumulated from all the nuclear emissions of stars over the course of cosmic history, at which time they will start detecting weakly interacting particles as intended: neutrinos. Those aren’t the dark matter, but what are the odds that the first of those neutrino detections will be eagerly misinterpreted as dark matter?
Finally, the question of the year: why does MOND get any prediction right? To provide a satisfactory answer to this, one must come up with a physical model that provides a compelling explanation for the phenomena and has the same ability as MOND to make novel predictions. Just building a post-hoc model to match the data, which is the most common approach, doesn’t provide a satisfactory, let alone a compelling, explanation for the phenomenon, and provides no predictive power at all. If it did, we could have predicted MOND-like phenomenology and wouldn’t have to build these models after the fact.
So far, none of these three things have been clearly satisfied. The greatest danger to MOND comes from MOND itself: the residual mass discrepancy in clusters, the tension in Galactic data (some of which favor MOND, other of which don’t), and the apparent absence of dark matter in some galaxies. While these are real problems, they are also of the scale that is expected in the normal course of science: there are always tensions and misleading tidbits of information; I personally worry the most about the Galactic data. But even if my first point is satisfied and MOND fails on its own merits, that does not make dark matter better.
A large segment of the scientific community seems to suffer a common logical fallacy: any problem with MOND is seen as a success for dark matter. That’s silly. One has to evaluate the predictions of dark matter for the same observation to see how it fares. My experience has been that observations that are problematic for MOND are also problematic for dark matter. The latter often survives by not making a prediction at all, which is hardly a point in its favor.
Other situations are just plain weird. For example, it is popular these days to cite the absence of dark matter in some ultradiffuse galaxies as a challenge to MOND, which they are. But neither does it make sense to have galaxies without dark matter in a universe made of dark matter. Such a situation can be arranged, but the circumstances are rather contrived and usually involve some non-equilibrium dynamics. That’s fine; that can happen on rare occasions, but disequilibrium situations can happen in MOND too (the claims of falsification inevitably assume equilibrium). We can’t have it both ways, permitting special circumstances for one theory but not for the other. Worse, some examples of galaxies that are claimed to be devoid of dark matter are as much a problem for LCDM as for MOND. A disk galaxy devoid of either can’t happen; we need something to stabilize disks.
So where do we go from here? Who knows! There are fundamental questions that remain unanswered, and that’s a good thing. There is real science yet to be done. We can make progress if we stick to the scientific method. There is more to be done than measuring cosmological parameters to the sixth place of decimals. But we have to start by setting standards for falsification. If there is no observation or experimental result that would disabuse you of your current belief system, then that belief system is more akin to religion than to science.
1There are a few ideas, like superfluid dark matter, that try to automatically produce MOND phenomenology. This is what needs to happen. It isn’t clear yet whether these ideas work, but reproducing the MOND phenomenology naturally is a minimum standard that has to be met for a model to be viable. Run of the mill CDM models that invoke feedback do not meet this standard. They can always be made to reproduce the data once observed, but not to predict it in advance as MOND does.
2There is a common refrain that “MOND fits rotation curves and nothing else.” This is a myth, plain and simple. A good, old-fashioned falsehood sustained by the echo chamber effect. (That’s what I heard!) Seriously: if you are a scientist who thinks this, what is your source? Did it come from a review of MOND, or from idle chit-chat? How many MOND papers have you read? What do you actually know about it? Ignorance is not a strong position from which to draw a scientific conclusion.
3Like most of the community, I have invested considerably more effort in dark matter than in MOND. Where I differ from much of the galaxy formation community* is in admitting when those efforts fail. There is a temptation to slap some lipstick on the dark matter pig and claim success just to go along to get along, but what is the point of science if that is what we do when we encounter an inconvenient result? For me, MOND has been an incredibly inconvenient result. I would love to be able to falsify it, but so far intellectual honesty forbids.
*There is a widespread ethos of toxic positivity in the galaxy formation literature, which habitually puts a more positive spin on results than is objectively warranted. I’m aware of at least one prominent school where students are taught “to be optimistic” and omit mention of caveats that might detract from the a model’s reception. This is effective in a careerist sense, but antithetical to the scientific endeavor.
4The word “falsification” carries a lot of philosophical baggage that I don’t care to get into here. The point is that there must be a way to tell if a theory is wrong. If there is not, we might as well be debating the number of angels that can dance on the head of a pin.
I would like to write something positive to close out the year. Apparently, it is not in my nature, as I am finding it difficult to do so. I try not to say anything if I can’t say anything nice, and as a consequence I have said little here for weeks at a time.
Still, there are good things that happened this year. JWST launched a year ago. The predictions I made for it at that time have since been realized. There have been some bumps along the way, with some of the photometric redshifts for very high z galaxies turning out to be wrong. They have not all turned out to be wrong, and the current consensus seems to be converging towards acceptance of there existing a good number of relatively bright galaxies at z > 10. Some of these have been ‘confirmed’ by spectroscopy.
I remain skeptical of some of the spectra as well as the photometric redshifts. There isn’t much spectrum to see at these rest frame ultraviolet wavelengths. There aren’t a lot of obvious, distinctive features in the spectra that make for definitive line identifications, and the universe is rather opaque to the UV photons blueward of the Lyman break. Here is an example from the JADES survey:
Images and spectra of z > 10 galaxy candidates from JADES. [Image Credits: NASA, ESA, CSA, M. Zamani (ESA/Webb), Leah Hustak (STScI); Science Credits: Brant Robertson (UC Santa Cruz), S. Tacchella (Cambridge), E. Curtis-Lake (UOH), S. Carniani (Scuola Normale Superiore), JADES Collaboration]
Despite the lack of distinctive spectral lines, there is a clear shape that is ramping up towards the blue until hitting a sharp edge. This is consistent with the spectrum of a star forming galaxy with young stars that make a lot of UV light: the upward bend is expected for such a population, and hard to explain otherwise. The edge is cause by opacity: intervening gas and dust gobbles up those photons, few of which are likely to even escape their host galaxy, much less survive the billions of light-years to be traversed between there-then and here-now. So I concur that the most obvious interpretation of these spectra is that of high-z galaxies even if we don’t have the satisfaction of seeing blatantly obvious emission lines like C IV or Mg II (ionized species of carbon and magnesium that are frequently seen in the spectra of quasars). [The obscure nomenclature dates back to nineteenth century laboratory spectroscopy. Mg I is neutral, Mg II singly ionized, C IV triply ionized.]
Even if we seem headed towards consensus on the reality of big galaxies at high redshift, the same cannot yet be said about their interpretation. This certainly came as a huge surprise to astronomers not me. The obvious interpretation is the theory that predicted this observation in advance, no?
Apparently not. Another predictable phenomenon is that people will self-gaslight themselves into believing that this was expected all along. I have been watching in real time as the community makes the transition from “there is nothing above redshift 7” (the prediction of LCDM contemporary with Bob Sanders’s MOND prediction that galaxy mass objects form by z=10) to “this was unexpected!” and is genuinely problematic to “Nah, we’re good.” This is the same trajectory I’ve seen the community take with the cusp-core problem, the missing satellite problem, the RAR, the existence of massive clusters of galaxies at surprisingly high redshift, etc., etc. A theory is only good to the extent that its predictions are not malleable enough to be made to fit any observation.
As I was trying to explain on twitter that individually high mass galaxies had not been expected in LCDM, someone popped into my feed to assert that they had multiple simulations with galaxies that massive. That certainly had not been the case all along, so this just tells me that LCDM doesn’t really make a prediction here that can’t be fudged (crank up the star formation efficiency!). This is worse than no prediction at all: you can never know that you’re wrong, as you can fix any failing. Worse, it has been my experience that there is always someone willing to play the role of fixer, usually some ambitious young person eager to gain credit for saving the most favored theory. It works – I can point to many Ivy league careers that followed this approach. They don’t even have to work hard at it, as the community is predisposed to believe what they want to hear.
These are all reasons why predictions made in advance of the relevant observation are the most valuable.
That MOND has consistently predicted, in advance, results that were surprising to LCDM is a fact that the community apparently remains unaware of. Communication is inefficient, so for a long time I thought this sufficed as an explanation. That is no longer the case; the only explanation that fits the sociological observations is that the ignorance is willful.
“It is difficult to get a man to understand something, when his salary depends on his not understanding it.”
Upton Sinclair
We have been spoiled. The last 400 years has given us the impression that science progresses steadily and irresistibly forward. This is in no way guaranteed. Science progresses in fits and starts; it only looks continuous when the highlights are viewed in retrospective soft focus. Progress can halt and even regress, as happened abruptly with the many engineering feats of the Romans with the fall of their empire. Science is a human endeavor subject to human folly, and we might just as easily have a thousand years of belief in invisible mass as we did in epicycles.
Despite all this, I remain guardedly optimistic that we can and will progress. I don’t know what the right answer is. The first step is to let go of being sure that we do.
I’ll end with a quote pointed out to me by David Merritt that seems to apply today as it did centuries ago:
“The scepticism of that generation was the most uncompromising that the world has known; for it did not even trouble to deny: it simply ignored. It presented a blank wall of perfect indifference alike to the mysteries of the universe and to the solutions of them.”
We are visual animals. What we see informs our perception of the world, so it often helps to make a sketch to help conceptualize difficult material. When first confronted with MOND phenomenology in galaxies that I had been sure were dark matter dominated, I made a sketch to help organize my thoughts. Here is a scan of the original dark matter tree that I drew on a transparency (pre-powerpoint!) in 1995:
The original dark matter tree.
At the bottom are the roots of the problem: the astronomical evidence for mass discrepancies. From these grow the trunk, which splits into categories of possible solutions, which in turn branch into ever more specific possibilities. Most of these items were already old news at the time: I was categorizing, not inventing. Indeed, some things have been rebranded over time without changing all that much, with strange nuggets now being known as macros (a generalization to describe dark matter candidates of nuclear density) and asymmetric gravity becoming MOG. The more things change, the more they stay the same.
I’ve used this picture many times in talks, both public and scientific. It helps to focus the mind. I updated it for the 2012 review Benoit Famaey wrote (see our Fig. 1), but I don’t think I really improved on the older version, which Don Lincoln had adapted for the cover illustration of an issue of Physics Teacher (circa 2013), with some embellishment by their graphic artists. That’s pretty good, but I prefer my original.
Though there are no lack of buds on the tree, there have certainly been more ideas for dark matter candidates over the past thirty years, so I went looking to see if someone had attempted a similar exercise to categorize or at least corral all the ideas people have considered. Tim Tait made one such figure, but you have to already be an expert to make any sense of it, it being a sort of Venn diagram of the large conceptual playground that is theoretical particle physics.
This is nice: well organized and pleasantly symmetric, and making good use of color to distinguish different types of possibilities. One can recognize many of the same names from the original tree like MACHOs and MOND, along with newer, related entities like Macros and TeVeS. Interestingly, WIMPs are not mentioned, despite dominating the history of the field. They are subsumed under supersymmetry, which is now itself just a sub-branch of weak-scale possibilities rather than the grand unified theory of manifest inevitability that it was once considered to be. It is a sign of how far we have come that the number one candidate, the one that remains the focus of dozens of large experiments, doesn’t even come up by name. It is also a sign of how far we have yet to go that it seems preferable to many to invent new dark matter candidates than take seriously alternatives that have had much greater predictive success.
A challenge one faces in doing this exercise is to decide which candidates deserve mention, and which are just specific details that should be grouped under some more major branch. As a practical matter, it is impossible to wedge everything in, nor does every wild idea we’ve ever thought up deserve equal mention: Kaluza-Klein dark matter is not a coequal peer to WIMPs. But how do we be fair about making that call? It may not be possible.
I wanted to see how the new diagram mapped to the old tree, so I chopped it up and grafted each piece onto the appropriate branch of the original tree:
New blossoms on the old dark matter tree.
This works pretty well. It looks like the tree has blossomed with more ideas, which it has. There are more possibilities along well-established branches, and entirely new branches that I could only anticipate with question marks that allowed for the possibility of things we had not yet thought up. The tree is getting bushy.
Ultimately, the goal is not to have an ever bushier tree, but rather the opposite: we want to find the right answer. As an experimentalist, one wants to either detect or exclude specific dark matter candidates. As an scientist, I want to apply the wealth of observational knowledge we have accumulated like a chainsaw in the hands of an overzealous gardener to hack off misleading branches until the tree has been pruned down to a single branch, the one (and hopefully only one) correct answer.
As much as I like Bertone & Tait’s hexagonal image, it is very focused on ideas in particle physics. Five of the six branches are various forms of dark matter, while the possibility of modified gravity is grudgingly acknowledged in only one. It is illustrated as a dull grey that is unlike the bright, cheerful colors granted to the various flavors of dark matter candidates. To be sure, there are more ideas for solutions to the mass discrepancy problem from the particle physics than anywhere else, but that doesn’t mean they all deserve equal mention. One looking at this diagram might get the impression that the odds of dark matter:modified gravity are 5:1, which seems at once both biased against the latter and yet considerably more generous than its authors likely intended.
There is no mention at all of the data at the roots of the problem. That is all subsumed in the central DARK MATTER, as if we’re looking down at the top of the tree and recognize that it must have a central trunk, but cannot see its roots. This is indeed an apt depiction of the division between physics and astronomy. Proposed candidates for dark matter have emerged primarily from the particle physics community, which is what the hexagon categorizes. It takes for granted the evidence for dark matter, which is entirely astronomical in nature. This is not a trivial point; I’ve often encountered particle physicists who are mystified that astronomers have the temerity of think they can contribute to the dark matter debate despite 100% (not 90%, nor 99%, nor even 99.9%, but 100%) of the evidence for mass discrepancies stemming from observations of the sky. Apparently, our job was done when we told them we needed something unseen, and we should remain politely quiet while the Big Brains figure it out.
For a categorization of solutions, I suppose it is tolerable if dangerous divorced from the origins of the problem to leave off the evidence. There is another problem with placing DARK MATTER at the center. This is a linguistic problem that raises deep epistemological issues that most scientists working in the field rarely bother to engage with. Words matter; the names we use frame how we think about the problem. By calling it the dark matter problem, we presuppose the answer. A more appropriate term might be mass discrepancy, which was in use for a while by more careful-minded people, but it seems to have fallen into disuse. Dark matter is easier to say and sounds way more cool.
Jacob Bekenstein pointed out that an even better term would be acceleration discrepancy. That’s what we measure, after all. The centripetal acceleration in spiral galaxies exceeds that predicted by the observed distribution of visible matter. Mass is an inference, and a sloppy one at that: dynamical data only constrain the mass enclosed by the last measured point. The total mass of a dark matter halo depends on how far it extends, which we never observe because the darn stuff is invisible. And of course we only infer the existence of dark matter by assuming that the force law is correct. That gravity as taught to us by Einstein and Newton should apply to galaxies seems like a pretty darn good assumption, but it is just that. By calling it the dark matter problem, we make it all about unseen mass and neglect the possibility that the inference might go astray with that first, basic assumption.
So I’ve made a new picture, placing the acceleration discrepancy at the center where it belongs. The astronomical observations that inform the problem are on the vertical axis while the logical possibilities for physics solutions are on the horizontal axis. I’ve been very spare in filling in both: I’m trying to trace the logical possibilities with a minimum of bias and clutter, so I’ve retained some ideas that are pretty well excluded.
For example, on the dark matter side, MACHOs are pretty well excluded at this point, as are most (all?) dark matter candidates composed of Standard Model particles. Normal matter just doesn’t cut it, but I’ve left that sector in as a logical possibility that was considered historically and shouldn’t be forgotten. On the dynamical side, one of the first thoughts is that galaxies are big so perhaps the force law changes at some appropriate scale much large than the solar system. At this juncture, we have excluded all modifications to the force law that are made at a specific length scale.
The acceleration discrepancy diagram.
There are too many lines of observational evidence to do justice to here. I’ve lumped an enormous amount of it into a small number of categorical bins. This is not ideal, but some key points are at least mentioned. I invite the reader to try doing the exercise with pencil and paper. There are serious limits imposed by what you can physically display in a font the eye can read with a complexity limited to that which does not make the head explode. I fear I may already be pushing both.
I have made a split between dynamical and cosmological evidence. These tend to push the interpretation one way or the other, as hinted by the colors. Which way one goes depends entirely on how one weighs rather disparate lines of evidence.
I’ve also placed the things that were known from the outset of the modern dark matter paradigm closer to the center than those that were not. That galaxies and clusters of galaxies needed something more than meets the eye was known, and informed the need for dark matter. That the dynamics of galaxies over a huge range of mass, size, surface brightness, gas fraction, and morphology are organized by a few simple empirical relations was not yet known. The Baryonic Tully-Fisher Relation (BTFR) and the Radial Acceleration Relation (RAR) are critical pieces of evidence that did not inform the construction of the current paradigm, and are not satisfactorily explained by it.
Similarly for cosmology, the non-baryonic cold dark matter paradigm was launched by the observation that the dynamical mass density apparently exceeds that allowed for normal matter by primordial nucleosynthesis. This, together with the need to grow the observed large scale structure from the very smooth initial condition indicated by the cosmic microwave background (CMB), convinced nearly everyone (including myself) that there must be some new form of non-baryonic dark matter particle outside the realm of the Standard Model. Detailed observations of the power spectra of both galaxies and the CMB are important corroborating observations that did not yet exist at the time the idea took hold. We also got our predictions for these things very wrong initially, hence the need to change from Standard CDM to Lambda CDM.
Most of the people I have met who work on dark matter candidates seem to be well informed of cosmological constraints. In contrast, their knowledge of galaxy dynamics often seems to start and end with “rotation curves are flat.” There is quite a lot more to it than that. But, by and large, they stopped listening at “therefore we need dark matter” and were off and running with ideas for what it could be. There is a need to reassess the viability of these ideas in the light of the BTFR and the RAR.
People who work on galaxy dynamics are concerned with the obvious connections between dynamics and the observed stars and are inclined to be suspicious of the cosmological inference requiring non-baryonic dark matter. Over the years, I have repeatedly been approached by eminent dynamicists who have related in hushed tones, less the cosmologists overhear, that the dark matter must be baryonic. I can understand their reticence, since I was, originally, one of those people who they didn’t want to have overhear. Baryonic dark mater was crazy – we need more mass than is allowed by big bang nucleosynthesis! I usually refrained from raising this issue, as I have plenty of reasons to sympathize, and try to be a sympathetic ear even when I don’t. I did bring it up in an extended conversation with Vera Rubin once, who scoffed that the theorists were too clever by half. She reckoned that if she could demonstrate that Ωm = 1 in baryons one day, that they would have somehow fixed nucleosynthesis by the next. Her attitude was well-grounded in experience.
A common attitude among advocates of non-baryonic dark matter is that the power spectrum of the CMB requires its existence. Fits to the data require a non-baryonic component at something like 100 sigma. That’s pretty significant evidence.
The problem with this attitude is that it assumes General Relativity (GR). That’s the theory in which the fits are made. There is, indeed, no doubt that the existence of cold dark matter is required in order to make the fits in the context of GR: it does not work without it. To take this as proof of the existence of cold dark mater is entirely circular logic. Indeed, that we have to invent dark matter as a tooth fairy to save GR might be interpreted as evidence against it, or at least as an indication that there might exist a still more general theory.
Nevertheless, I do have sympathy for the attitude that any idea that is going to work has to explain all the data – including both dynamical and cosmological evidence. Where one has to be careful is to assume that the explanation we currently have is unique – so unique that no other theory could ever conceivably explain it. By that logic, MOND is the only theory that uniquely predicted both the BTFR and the RAR. So if we’re being even-handed, cold dark matter is ruled out by the dynamical relations identified after its invention at least as much as its competitors are excluded by the detailed, later measurement of the power spectrum of the CMB.
If we believe all the data, and hold all theories to the same high standard, none survive. Not a single one. A common approach seems to be to hold one’s favorite theory to a lower standard. I will not dignify that with a repudiation. The challenge with data both astronomical and cosmological, is figuring out what to believe. It has gotten better, but you can’t rely on every measurement being right, or – harder to bear in mind – actually measure what you want it to measure. Do the orbits of gas clouds in spiral galaxies trace the geodesics of test particles in perfectly circular motion? Does the assumption of hydrostatic equilibrium in the intracluster medium (ICM) of clusters of galaxies provide the same tracer of the gravitational potential as dynamics? There is an annoying offset in the acceleration scale measured by the two distinct methods. Is that real, or some systematic? It seems to be real, but it is also suspicious for appearing exactly where the change in method occurs.
The characteristic acceleration scale in extragalactic systems as a function of their observed baryonic mass. This is always close to the ubiquitous scale of 10-10 m/s/s first recognized by Milgrom. There is a persistent offset for clusters of galaxies that occurs where we switch from dynamical to hydrostatic tracers of the potential (Fig. 48 from Famaey & McGaugh 2012).
One will go mad trying to track down every conceivable systematic. Trust me, I’ve done the experiment. So an exercise I like to do is to ask what theory minimizes the amount of data I have to ignore. I spent several years reviewing all the data in order to do this exercise when I first got interested in this problem. To my surprise, it was MOND that did best by this measure, not dark matter. To this date, clusters of galaxies remain the most problematic for MOND in having a discrepant acceleration scale – a real problem that we would not hesitate to sweep under the rug if dark matter suffered it. For example, the offset the EAGLE simulation requires to [sort of] match the RAR is almost exactly the same amplitude as what MOND needs to match clusters. Rather than considering this to be a problem, they apply the required offset and call it natural to have missed by this much.
Most of the things we call evidence for dark matter are really evidence for the acceleration discrepancy. A mental hang up I had when I first came to the problem was that there’s so much evidence for dark matter. That is a misstatement stemming from the linguistic bias I noted earlier. There’s so much evidence for the acceleration discrepancy. I still see professionals struggle with this, often citing results as being contradictory to MOND that actually support it. They seem not to have bothered to check, as I have, and are content to repeat what they heard someone else assert. I sometimes wonder if the most lasting contribution to science made by the dark matter paradigm is as one giant Asch conformity experiment.
If we repeat today the exercise of minimizing the amount of data we have to disbelieve, the theory that fares best is the Aether Scalar Tensor (AeST) theory of Skordis & Zlosnik. It contains MOND in the appropriate limit while also providing an excellent fit to the power spectrum of galaxies and the CMB (see also the updated plots in their paper). Hybrid models struggle to do both while the traditional approach of simply adding mass in new particles does not provide a satisfactory explanation of the MOND phenomenology. They can be excluded unless we indulge in the special pleading that invokes feedback or other ad hoc auxiliary hypotheses. Similarly, more elaborate ideas like self-interacting dark matter were dead on arrival for providing a mechanism to solve the wrong problem: the cores inferred in dark matter halos are merely a symptom of the more general MONDian phenomenology; the proposed solution addresses the underlying disease about as much as a band-aid helps an amputation.
Does that mean AeST is the correct theory? Only in the sense that MOND was the best theory when I first did this exercise in the previous century. The needle has swung back and forth since then, so it might swing again. But I do hope that it is a step in a better direction.
Triton Station 