This is what I hope will be the final installment in a series of posts describing the results published in McGaugh et al. (2024). I started by discussing the timescale for galaxy formation in LCDM and MOND which leads to different and distinct predictions. I then discussed the observations that constrain the growth of stellar mass over cosmic time and the related observation of stellar populations that are mature for the age of the universe. I then put on an LCDM hat to try to figure out ways to wriggle out of the obvious conclusion that galaxies grew too massive too fast. Exploring all the arguments that will be made is the hardest part, not because they are difficult to anticipate, but because there are so many* options to consider. This leads to many pages of minutiae that no one ever seems to read+, so one of the options I’ve discussed (e.g., super-efficient star formation) will likely emerge as the standard picture even if it comes pre-debunked.
The emphasis so far has been on the evolution of the stellar masses of galaxies because that is observationally most accessible. That gives us the opportunity to wriggle, because what we really want to measure to test LCDM is the growth of [dark] mass. This is well-predicted but invisible, so we can always play games to relate light to mass.
Galaxy Kinematics
What we really want to know is the underlying mass. It is reasonable to expect that the light traces this mass, but is there another way to assess it? Yes: kinematics. The orbital speeds of objects in galaxies trace the total potential, including the dark matter. So, how massive were early galaxies? How does that evolve with redshift?
The rotation curve for NGC 6946 shows a number of well-established characteristics for nearby galaxies, including the dominance of baryons at small radii in high surface brightness galaxies and the famous flat outer portion of the rotation curve. Even when stars contribute as much mass as allowed by the inner rotation curve (“maximum disk“), there is a need for something extra further out (i.e., dark matter or MOND). In the case of dark matter, the amplitude of flat rotation is typically interpreted as being indicative& of halo mass.
So far, the rotation curves of high redshift galaxies look very much like those of low redshift galaxies. There are some fast rotators at high redshift as well. Here is an example observed by Neeleman et al. (2020), who measure a flat rotation speed of 272 km/s for DLA0817g at z = 4.26. That’s more massive than either the Milky Way (~200 km/s) or Andromeda (~230 km/s), if not quite as big as local heavyweight champion UGC 2885 (300 km/s). DLA0817g looks to be a disk galaxy that formed early and is sedately rotating only 1.4 Gyr after the Big Bang. It is already massive at this time: not at all the little nuggets we expect from the CDM merger tree above.
This is anecdotal, of course, but there are a good number of similar cases that are already known. For example, the kinematics of ALESS 073.1 at z ≈ 5 indicate the presence of a massive stellar bulge as well as a rapidly rotating disk (Lelli et al. 2021). A similar case has been observed at z ≈ 6 (Tripodi et al. 2023). These kinematic observations indicate the presence of mature, massive disk galaxies well before they were expected to be in place (Pillepich et al. 2019; Wardlow 2021). The high rotation speeds observed in early disk galaxies sometimes exceed 250 (Neeleman et al. 2020) or even 300 km s−1 (Nestor Shachar et al. 2023; Wang et al. 2024), comparable to the most massive local spirals (Noordermeer et al. 2007; Di Teodoro et al. 2021, 2023). That such rapidly rotating galaxies exist at high redshift indicates that there is a lot of mass present, not just light. We can’t just tweak the mass-to-light ratio of the stars to explain the photometry and also explain the kinematics.
In a seminal galaxy formation paper, Mo, Mao, & White (1998) predicted that “present-day disks were assembled recently (at z ≤ 1).” Today, we see that spiral galaxies are ubiquitous in JWST images up to z ∼ 6 (Ferreira et al. 2022, 2023; Kuhn et al. 2024). The early appearance of massive, dynamically cold (Di Teodoro et al. 2016; Lelli et al. 2018, 2023; Rizzo et al. 2023) disks in the first few billion years after the Big Bang is contradictory the natural prediction of ΛCDM. Early disks are expected to be small and dynamically hot (Dekel & Burkert 2014; Zolotov et al. 2015; Krumholz et al. 2018; Pillepich et al. 2019), but they are observed to be massive and dynamically cold. (Hot or cold in this context means a high or low amplitude of the velocity dispersion relative to the rotation speed; the modern Milky Way is cold with σ ~ 20 km/s and Vc ~ 200 km/s.) Understanding the stability and longevity of dynamically cold spiral disks is foundational to the problem.
Kinematic Scaling Relations
Beyond anecdotal cases, we can check on kinematic scaling relations like Tully–Fisher. These are expected to emerge late and evolve significantly with redshift in LCDM (e.g., Glowacki et al. 2021). In MOND, the normalization of the baryonic Tully–Fisher relation is set by a0, so is immutable for all time if a0 is constant. Let’s see what the data say:
Not much to see: the data from Nestor Shachar et al. (2023) show no clear indication of evolution. The same can be said for the dark matter fraction-surface brightness relation. (Glad to see that being plotted after I pointed it out.) The local relations are coincident with those at higher redshift for both relations within any sober assessment of the uncertainties – exactly what we measure and how matters at this level, and I’m not going to attempt to disentangle all that here. Neither am I about to attempt to assess the consistency (or lack thereof) with either LCDM or MOND; the data simply aren’t good enough for that yet. It is also not clear to me that everyone agrees on what LCDM predicts.
What I can do is check empirically how much evolution there is within the 100-galaxy data set of Nestor Shachar et al. (2023). To do that, I fit a line to their data (the left panel above) and measure the residuals: for a given rotation speed, how far is each galaxy from the expected mass? To compare this with the stellar masses discussed previously, I normalize those residuals to the same M** = 9 x 1010 M☉. If there is no evolution, the data will scatter around a constant value as function of redshift:
The data scatter around a constant value as function of redshift: there is no perceptible evolution.
The kinematic data for rotating galaxies tells much the same story as the photometric data for galaxies in clusters. The are both consistent with a monolithic model that gathered together the bulk of the baryonic mass early on, and evolved as an island universe for most of the history of the cosmos. There is no hint of the decline in mass with redshift predicted by the LCDM simulations. Moreover, the kinematics trace mass, not just light. So while I am careful to consider the options for LCDM, I don’t know how we’re gonna get out of this one.
Empirically, it is an important observation that there is no apparent evolution in the baryonic Tully-Fisher relation out to z ~ 2.5. That’s a lookback time of ~11 Gyr, so most of cosmic history. That means that whatever physics sets the relation did so early. If the physics is MOND, this absence of evolution implies that a0 is constant. There is some wiggle room in that given all the uncertainties, but this already excludes the picture in which a0 evolves with the expansion rate through the coincidence a0 ~ cH0. That much evolution would be readily perceptible if H(z) evolves as it appears to do. In contrast, the coincidence a0 ~ c2Λ1/2 remains interesting since the cosmological constant is constant. Perhaps this is just a coincidence, or perhaps it is a hint that the anomalous acceleration of the expansion of the universe is somehow connected with the anomalous acceleration in galaxy dynamics.
Though I see no clear evidence for evolution in Tully-Fisher to date, it remains early days. For example, a very recent paper by Amvrosiadis et al. (2025) does show a hint of evolution in the sense of an offset in the normalization of the baryonic Tully-Fisher relation. This isn’t very significant, being different by less than 2σ; and again we find ourselves in a situation where we need to take a hard look at all the assumptions and population modeling and velocity measurements just to see if we’re talking about the same quantities before we even begin to assess consistency or the lack thereof. Nevertheless, it is an intriguing result. There is also another interesting anecdotal case: one of their highest redshift objects, ALESS 071.1 at z = 3.7, is also the most massive in the sample, with an estimated stellar mass of 2 x 1012 M☉. That is a crazy large number, comparable to or maybe larger than the entire dark matter halo of the Milky Way. It falls off the top of any of the graphs of stellar mass we discussed before. If correct, this one galaxy is an enormous problem for LCDM regardless of any other consideration. It is of course possible that this case will turn out to be wrong for some reason, so it remains early days for kinematics at high redshift.
Cluster Kinematics
It is even earlier days for cluster kinematics. First we have to find them, which was the focus of Jay Franck’s thesis. Once identified, we have to estimate their masses with the available data, which may or may not be up to the task. And of course we have to figure out what theory predicts.
LCDM makes a clear prediction for the growth of cluster mass. This work out OK at low redshift, in the sense that the cluster X-ray mass function is in good agreement with LCDM. Where the theory struggles is in the proclivity for the most massive clusters to appear sooner in cosmic history than anticipated. Like individual galaxies, they appear too big too soon. This trend persisted in Jay’s analysis, which identified candidate protoclusters at higher redshifts than expected. It also measured velocity dispersions that were consistently higher than found in simulations. That is, when Jay applied the search algorithm he used on the data to mock data from the Millennium simulation, the structures identified there had velocity dispersions on average a factor of two lower than seen in the data. That’s a big difference in terms of mass.
At this juncture, there is no way to know if the protocluster candidates Jay identified are or will become bound structures. We made some probability estimates that can be summed up as “some are probably real, but some probably are not.” The relative probability is illustrated by the size of the points in the plot above; the big blue points are the most likely to be real clusters, having at least ten galaxies at the same place on the sky at the same redshift, all with spectroscopically measured redshifts. Here the spectra are critical; photometric redshifts typically are not accurate enough to indicate that galaxies that happen to be nearby to each other on the sky are also that close in redshift space.
The net upshot is that there are at least some good candidate clusters at high redshift, and these have higher velocity dispersions than expected in LCDM. I did the exercise of working out what the equivalent mass in MOND would be, and it is about the same as what we find for clusters at low redshift. This estimate assumes dynamical equilibrium, which is very far from guaranteed. But the time at which these structures appear is consistent with the timescale for cluster formation in MOND (a couple Gyr; z ~ 3), so maybe? Certainly there shouldn’t be lots of massive clusters in LCDM at z ~ 3.
Kinematic Takeaways
While it remains early days for kinematic observations at high redshift, so far these data do nothing to contradict the obvious interpretation of the photometric data. There are mature, dynamically cold, fast rotating spiral galaxies in the early universe that were predicted not to be there by LCDM. Moreover, kinematics traces mass, not just light, so all the wriggling we might try to explain the latter doesn’t help with the former. The most obvious interpretation of the kinematic data to date is the same as that for the photometric data: galaxies formed early and grew massive quickly, as predicted a priori by MOND.
*The papers I write that cover both theories always seem to wind up lopsided in favor of LCDM in terms of the bulk of their content. That happens because it takes many pages to discuss all the ins and outs. In contrast, MOND just gets it right the first time, so that section is short: there’s not much more to say than “Yep, that’s what it predicted.”
+I’ve yet not heard directly any criticisms of our paper. The criticisms that I’ve heard second or third hand so far almost all fall in the category of things we explicitly discussed. That’s a pretty clear tell that the person leveling the critique hasn’t bothered to read it. I don’t expect everyone to agree with our take on this or that, but a competent critic would at least evince awareness that we had addressed their concern, even if not to their satisfaction. We rarely seem to reach that level: it is much easier to libel and slander than engage with the issues.
The one complaint I’ve heard so far that doesn’t fall in the category of things-we-already-discussed is that we didn’t do hydrodynamic simulations of star formation in molecular gas. That is a red herring. To predict the growth of stellar mass, all we need is a prescription for assembling mass and converting baryons into stars; this is essentially a bookkeeping exercise that can be done analytically. If this were a serious concern, it should be noted that most cosmological hydro-simulations also fail to meet this standard: they don’t resolve star formation, so they typically adopt some semi-empirical (i.e., data-informed) bookkeeping prescription for this “subgrid physics.”
Though I have not myself attempted to numerically simulate galaxy formation in MOND, Sanders (2008) did. More recently, Eappen et al. (2022) have done so, including molecular gas and feedback$ and everything. They find a star formation history compatible with the analytic models we discuss in our paper.
$Related detail: Eappen et al find that different feedback schemes make little difference to the end result. The deus ex machina invoked to solve all problems in LCDM is largely irrelevant in MOND. There’s a good physical reason for this: gravity in MOND is sourced by what you see; how it came to have its observed distribution is irrelevant. If 90% of the baryons are swept entirely out of the galaxy by some intense galactic wind, then they’re gone BYE BYE and don’t matter any more. In contrast, that is one of the scenarios sometimes invoked to form cores in dark matter halos that are initially cuspy: the departure of all those baryons perturbs the orbits of the dark matter particles and rearranges the structure of the halo. While that might work to alter halo structure, how it results in MOND-like phenomenology has never been satisfactorily explained. Mostly that is not seen as even necessary; converting cusp to core is close enough!
&Though we typically associate the observed outer velocity with halo mass, an important caveat is that the radius also matters: M ~ RV2, and most data for high redshift galaxies do not extend very far out in radius. Nevertheless, it takes a lot of mass to make rotation speeds of order 200 km/s within a few kpc, so it hardly matters if this is or is not representative of the dark matter halo: if it is all stars, then the kinematics directly corroborate the interpretation of the photometric data that the stellar mass is large. If it is representative of the dark matter halo, then we expect the halo radius to scale with the halo velocity (R200 ~ V200) so M200 ~ V2003 and again it appears that there is too much mass in place too early.
Interesting, the Baryonic Tully-Fisher Relation does evolve if you bin the galaxies according to their evolutionary stage. For example there is an offset in the BTFR for starburst galaxies, gas rich spirals, spirals and lenticular galaxies. The normalisation constant for starburst galaxies is higher than that for gas rich spirals, which in turn is higher than that for spirals and lenticular galaxies have the lowest. That is lenticular galaxies have higher rotational velocities for the same Baryonic mass compared to younger galaxies. This behavior is governed by the evolving baryonic Tully Fisher relation
v=e^Ht. (GMHc/2π)^(1/4)
You can find more details here https://arxiv.org/abs/2501.04065
So much to think about here! Can you explain the reasoning a bit more for drawing any conclusions about a relationship at high z between cH0 or the cosmological constant and a0, based on a present time measurement of a0?
I thought you said galaxy dynamics don’t seem to care about the universe at large. I am trying to wrap my head around whether we would need to hitch a ride with our telescope on the shrinking horizon of the universe to see any connection between these measures at z=2.5? I’m not suggesting there is no relation between them, but what is it that this measure rules out exactly?
H0 is the expansion rate of the universe that we measure now. That expansion rate need not remain the same for all time, and in general does not, so the Hubble “constant” is a misnomer: in general we have the Hubble parameter H(z). There are observational estimates of that, and it varies noticeably out to z~2. So if we try to force them to be equal, say 2 pi a0 = c H0, then if H varies with z, so must a: 2 pi a(z) = cH(z). What I’m not seeing is any evidence that a(z) varies as H(z).
But in order to measure a0 in galaxy dynamics, wouldn’t you have to first correct for the relative observer velocity, which then transforms away any a0 dependence on z?
There are many corrections, e.g., for inclination, the fraction of undetected gas, and the evolution of the stellar population. Those make me queasy about the mass axis; I’m amazed they’re in the same ballpark. On the velocity axis there is a (1+z) correction for the stretching caused by the expansion of the universe on top of the rotation signal, if that’s what you mean.
Yes, that is what I was generally thinking about the velocity correction. That’s pretty interesting about the mass axis corrections – how much total variability might you expect in the mass axis estimate? Secondly, what would your estimate be for the mass of the universe in the MOND paradigm?
Stellar pop mass estimates can be off by a factor of 2 locally; it gets worse at higher redshift. I don’t think it is that bad, and that the numbers come out as well as they do is encouraging, but it is a perpetual concern.
The mass of the universe is the baryon density (~5% of critical) times whatever volume you want to call the universe.
Thank you Dr. McGaugh for another excellent post. With bases loaded, the players awaiting further data accumulation and analysis, the MOND team appears to be on the verge of another home run.
“… there is a need for something extra further out (i.e., dark matter or MOND).” Can dark matter particles provide a satisfactory model for MOND? Put MOND charges on gravitons & gravitinos — then assume that the distribution of gravitinos approximately satisfies MOND. What is the refutation of the MOND charge hypothesis?
No, dark matter does not provides a satisfactory explanation for MOND, at least as we conventionally think of it. You are adding an additional, auxiliary hypothesis to it, that DM carries some sort of “MOND charge.” If one can do that so as to do as its name suggests, then by construction, you couldn’t tell the difference. There are hypotheses like this, e.g., the dipolar DM of Blanchet.
Can Q-balls describe cosmological and galactic dark matter?” by Susobhan Mandal
Abstract
Q-balls, which are localized, non-topological solitons, can be a bridge between the two hypotheses. Q-balls formed in the early Universe can mimic CDM at cosmological scales. Interestingly, Q-balls can exhibit MOND-like behavior in the late Universe at galactic scales, providing a unified framework.
https://arxiv.org/abs/2502.00821
Maybe? Sounds unlikely, but at least it is engaging with the problem.
In its simplest form, a Q-ball is constructed in a field theory of a complex scalar field ϕ {\displaystyle \phi }, in which Lagrangian is invariant under a global U ( 1 ) {\displaystyle U(1)} symmetry.
doesn’t many GR extension used complex scalar field for MOND?
Theorists love to add scalar fields. That is certainly one common approach to generalizing GR (either to make it MOND-like or just for the fun of it). Additionally, there is also the possibility of tensor fields. Hence theories with names like TeVeS (Tensor-Vector-Scalar) and AeST (Aether-Scalar-Tensor).
Simply adding a scalar field to a hypothetical DM particle need not have anything to do with MONDian gravitational effects. Indeed, the addition of such fields to GR to do so seems a bit tortured to me, but at least it is starting from the perspective of attempting to explain the observed phenomena. In contrast, the vast majority of the landscape of DM candidate particles people discuss nowadays have been been invented in ignorance of the observational phenomena. The common attitude among those who practice the craft seems to be limited to “cosmology needs dark matter” not “physics needs to rigorously reproduce flat rotation curves, the baryonic Tully-Fisher relation, and the radial acceleration relation” as it should be.
Maybe scalar fields play a role, but it seems like we are missing something deeper.
Is there any practical difference between adding a complex scalar field to GR to give rise to MOND or positing a scalar field in addition to the Standard Model like Q-balls that can supposedly reproduce MOND ?
Yes. Just having a scalar field around doesn’t guarantee this or that particular behavior; it depends on how it is implemented in a theory. I suspect that’s why they’re popular: they can be invoked to achieve any number of results. Heck, there is even a difference between TeVeS, which cannot be made to fit the CMB power spectrum, and AeST, which does fit it.
My guess is that (those few) string theorists who have looked at Professor Blanchet’s articles do not like his ideas.
“Gravitational polarization and the phenomenology of MOND”, Luc Blanchet, 2006
https://arxiv.org/abs/astro-ph/0605637
“Testing MOND in the Solar System” by Luc Blanchet & Jerome Novak, 2011, https://arxiv.org/abs/1105.5815
I think that the majority of string theorists are convinced that:
(a) String theory “predicts” quantum field theory with gravitons.
(b) String theory “predicts” general relativity theory.
(c) String theory predicts supersymmetry.
If one believes (a), (b), & (c), then MOND needs to be explained by a MONDian 5th force (probably involving supersymmetry).
My guess is that string theorists reject MOND & refuse to study MOND’s empirical successes because MOND has not been presented as empirical evidence for some form of supersymmetry.
A big selling point of string theory in the 1980s was that General Relativity “falls out” of it naturally. If instead MOND indicates that GR is not all that we need to know to proceed with constructing a quantum theory of gravity, then string theorists are playing solitaire with a deck that’s missing a few cards. That might explain why they have made zero progress in the past forty years.
Low-Acceleration Gravitational Anomaly from Bayesian 3D Modeling of Wide Binary Orbits: Methodology and Results with Gaia DR3
Authors: Kyu-Hyun Chae
arXiv:2502.09373
Recent statistical analyses of wide binaries have been performed only with sky-projected relative velocities vp in the pairs.These results show that gravitational anomaly is evident for gN≲10−9 m s−2 and Γ in the MOND regime (≲10−9.5 m s−2) agrees with the first-tier prediction (≈0.07) of MOND gravity theories.
I wish independent reviews of Wide Binary Orbits
I also wish independent reviews of wide binary orbits.
Kyu-Hyun makes some compelling points in his new work. I know he (and the other workers in the field) are making an earnest attempt to grapple with this issue. I hope they can sort it out.
Personally, it doesn’t matter to me which way this comes out. The MOND phenomenology is well established in galaxies. The only thing wide binaries can do is exclude dark matter or *some* flavors of MOND theories (i.e., gravity modified via modification of the Poisson equation but not modified inertia). I don’t think it is clear that they do any of that yet.
who would be qualified to do a independent reviews of wide binary orbits since Banik and Chae and Hernadez contradict one another, and what further observational data could confirm it.
clearly if wide binaries proves there is no dark matter, that would be very strong support for MOND. there are hypothesis that dark matter such as superfluid dark matter can explain MOND wide binaries would be a problem for such theories?
It depends on the predictions of each hypothesis.
Often, theories that attempt to mimic MOND only reproduce its low acceleration limit without having the equivalent of an external field effect. Wide binaries in the solar neighborhood are entirely in the EFE regime.
There are two reasons I am uninterested in engaging with this issue. One is that there are many additional complications about which I am not an expert. For example, when one gets to large enough separations, you do encounter other stars. It is possible that stars outside the binary have perturbed binaries at scales where we are assuming dynamical equilibrium, which may not hold. I hope there is an intermediate regime where this necessary assumption works, but that is highly nontrivial to assess. There are lots of issues like this that I am not qualified to sort out.
The second reason is that the importance of wide binaries is greatly exaggerated. The perfect unintentional experiment to test for MOND was already done in the dynamics of low surface brightness galaxies. By comparison, WBs are an afterthought.
There have already been hundreds of other tests of all sorts. Some of those come out poorly for MOND, but the vast majority of them support it. How do we decide which of these results are important? I’ve struggled with that, but the larger community has routinely ignored any result that gives the wrong answer (https://tritonstation.com/2022/02/08/a-script-for-every-observational-test/). Wide binaries would just be another example if there were three groups claiming MOND worked; they only get widely discussed because one of those groups gets the politically correct answer.
The community needs to catch up with the past several decades of results that it has ignored before it is worth debating WBs in any detail.
“… LCDM and MOND … different and distinct predictions …” LCDM without a MONDian 5th force seemingly implies MOND is empirically wrong (contrary to MOND’s successful predictions). However, there seems to be no compelling reason why LCDM inherently excludes a MONDian 5th force. There might be 8 plausible explanations for the “dark matter” phenomenon: MONDian 5th force and/or MOND inertia and/or a failure of Einstein’s equivalence principle. Does MOND inertia necessarily imply a failure of the equivalence principle? Consider this possibility: inertial mass-energy and gravitational mass-energy are indeed equivalent, but MOND inertia is a multiverse phenomenon that associates multiverse inertia with observable phenomena but does not associate multiverse inertia with mass-energy that occurs in the observable universe. What might rule out the preceding possibility?
I’m curious about how observational biases are taken into account in studying the early universe. For example, one possibility is that JWST only sees the extremely massive(luminous) *outliers* in the early universe, simply because the typical ones at that time appear too faint in our sky. Can you give some hints on the method employed to correct such biases?
Can I? Yes. Will I here? No… I’ve written a number of very technical papers on this; it doesn’t bear repeating in this forum. I’ll attempt a few brief comments.
For sure JWST sees the brightest beacons first – that is true for any astronomical survey. That’s one reason I’ve discussed extremal statistics. Even if everything JWST observes is atypical, it still sees far more than the most extreme extremes predicted in advance by LCDM simulations. There are various ways to wriggle out of this as I discussed in https://tritonstation.com/2025/01/23/the-fault-in-our-stars-blame-them-not-the-dark-matter/. The most plausible version I’ve heard is fluctuations in the instantaneous star formation rate stochastically pushing ordinary galaxies to the fore, as it were. I am skeptical that this can be a large enough effect to work out, and it has to be fine-tuned to keep the UV luminosity density constant as the galaxies making those UV photons brighten an dim suddenly like popcorn.
To discuss “typical” galaxies, one approach is to fit the luminosity function. That involves estimating the volume over which one could detect galaxies of a given luminosity (and surface brightness and color and etc.) and making a correction for it. That is a challenging technical task, and converting that to stellar mass for the highest redshift JWST objects is doubly challenging.
That said, this is not the biggest problem for LCDM, it’s just the most recent. We can do a much better job of constructing the stellar mass function at intermediate redshift. It was already clear from Jay Franck’s work 8 years ago, and from other work around then and since, that the *typical* galaxy at z ~ 4 is much brighter than it should be. That’s true even after aggressively excluding the brightest objects as potential AGN contaminants.
So yes, this is hard, but no, I don’t think we’re so easily fooled.
Friday (Feb 14) Preprint:
https://arxiv.org/pdf/2502.08885
Morphological Demographics of Galaxies at z ∼ 10–16
Ono et al
“Our results of 1) the log-normal re distribution, 2) the standard deviation value, and 3) a mean radial profile consistent with an exponential profile (n = 1.3 ± 0.6) suggest that galaxies at z ∼ 10–16 generally follow the classical galaxy disk formation scenario with a specific disk angular momentum fraction of jd/md ∼ 0.5–1”
This seems to extend the mature galaxy problem to the nth degree.
It does sound that way.
Reading through this paper a bit, their Fig. 19 is the basis of their statement about the specific angular momenta and disk fractions of disks at z > 10. This looks like a reasonable thing to do, but the quantities they quote are based on the model of Mo et al (1998) which is the paper that predicted that disks will form at z < 1.
Yes. Just having a scalar field around doesn’t guarantee this or that particular behavior; it depends on how it is implemented in a theory. I suspect that’s why they’re popular: they can be invoked to achieve any number of results. Heck, there is even a difference between TeVeS, which cannot be made to fit the CMB power spectrum, and AeST, which does fit it.
how viable is adding a new scalar field to the Standard Model implemented in a theory made to fit the CMB power spectrum via Q-balls acting like collisionless dark matter and to achieve MOND results like RAR for galaxy rotation curve ?
I’ve been reading the paper Jerry Jensen linked to on how very early galaxies seem unexpectedly similar nearby ones, but are much smaller. There’s a power-law that relates galaxy size to redshift, something similar has been used for 20 years, but the slope is adjusted on the way.
I’ve realised that a puzzle I mentioned might be easier to solve than I thought: looking for the curve as in VTC, there may be no need to bother with the time rate. (Once the curve is found, it can be applied to the time rate, which will then adjust what happened when, but the basic history is otherwise much the same.) You’re then left with the changes to the total mass, the same for all particles, which descends from a high starting value (the conceptual basis was linked to a few posts back). This is equivalent to the value of G changing instead.
So the puzzle I’ve been on seems to boil down to: what’s the equation that gives the curve for a changing value of G, related to z, which would reproduce the changes to galaxy size, and other things. It descends rapidly from a high value, and levels off at a value similar to the present one somewhere between z = 4 and z = 2.5. If that can be found, and if a few things then click into place – such as the accelerating expansion – I have a detailed conceptual basis to explain it.
I just found a paper that tries to explain the accelerating expansion via a changing value for G, https://arxiv.org/abs/2201.04629 (they’ve embedded it in standard theory, which may or may not be necessary). Their graph goes from z = 2.5 to z = 0, and looks like the curve I imagined, with loosely similar numbers (involving small differences in that redshift range), except for dipping below G[0] between z = 1.5 and z = 0.3. In the VTC picture some measurements need to be vetted for time rate dependency, such as cepheids, which includes timing a periodic effect. Those adjustments might change the curve – what I gave was an oversimplification, but it works as a starting point, and I always had trouble finding one before.
That early galaxies seem similar to nearby ones but are much smaller is what makes me worry about the angular size distance. Maybe they are similar and not smaller, we just infer that they are because we have the metric wrong. That is nightmare fuel for a cosmologist.