# How certain is dark matter?

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Robin04
How certain are scientists that the solution to the dark matter problem is a new, unknown particle (or more)? Theories that eliminate the need for new particle(s) and suggest modifications to the current understanding of gravity seem to get less attention. Why is that?

Homework Helper
Probably because there doesn't seem to be much "give" to Einstein's General of Relativity. It just seems to be spot on every time it is tested.

On the other hand, there has yet to be a good example of a galaxy that has significantly too much or too little Dark Matter - given its size.
If one could be found, it would strongly argue for the particle theory.
Here's an article that discusses a claim made earlier this year, a claim that is being hotly refuted:
https://www.scientificamerican.com/article/oddball-galaxy-find-puts-dark-matter-theory-to-the-test/

Robin04
Gold Member
2021 Award
How certain are scientists that the solution to the dark matter problem is a new, unknown particle (or more)? Theories that eliminate the need for new particle(s) and suggest modifications to the current understanding of gravity seem to get less attention. Why is that?
MOND theories have not done well against experimental evidence. In particular, for example, Google the "Bullet Cluster"

Marisa5, .Scott and Robin04
Robin04
Probably because there doesn't seem to be much "give" to Einstein's General of Relativity. It just seems to be spot on every time it is tested.
So it's more about confidence than actual arguments against theoretical modifications?

On the other hand, there has yet to be a good example of a galaxy that has significantly too much or too little Dark Matter - given its size.
Why would that be against the new matter hypothesis? It cannot be that dark matter density is not constant?

Mentor
So it's more about confidence than actual arguments against theoretical modifications?

It's not just that. Modified theories of gravity don't just affect cosmological observations. They affect all observations where gravity is involved. It's very, very difficult to find any modified theory of gravity that makes different predictions about cosmological observations (galaxy rotation curves, expansion of the universe) but doesn't make predictions different enough to be already falsified about other domains that involve gravity (such as the solar system).

Marisa5 and phinds
Gold Member
How certain are scientists that the solution to the dark matter problem is a new, unknown particle (or more)? Theories that eliminate the need for new particle(s) and suggest modifications to the current understanding of gravity seem to get less attention. Why is that?
Modified theories of gravity have gotten a lot of attention, and continue to do so. But most cosmologists think they're highly unlikely at this point because the evidence just doesn't point that way. Still, these kinds of theories have a certain kind of allure to many theorists, so there continues to be work in modified gravity theories to attempt to explain dark matter (and dark energy).

Mentor
2021 Award
Here's another hit for DM:
An anomalous emission component at energies of a few GeV and located towards the inner Galaxy is present in the Fermi-LAT data. It is known as the Fermi-LAT GeV excess. Using almost 8 years of data we reanalyze the characteristics of this excess with SkyFACT, a novel tool that combines image reconstruction with template fitting techniques. We find that an emission profile that traces stellar mass in the boxy and nuclear bulge provides the best description of the excess emission, providing strong circumstantial evidence that the excess is due to a stellar source population in the Galactic bulge. We find a luminosity to stellar mass ratio of ##(2.1±0.2)×10^{27} \,erg\,s^{-1}\,M^{-1}_⊙## for the boxy bulge, and of ##(1.4±0.6)×10^{27}\,erg\,s^{-1}\,M^{-1}_⊙## for the nuclear bulge. Stellar mass related templates are preferred over conventional DM profiles with high statistical significance.
preprint (11/13/17) https://arxiv.org/abs/1711.04778
publication (08/06/18), paywall https://www.nature.com/articles/s41550-018-0531-z

Gold Member
Here's another hit for DM:

preprint (11/13/17) https://arxiv.org/abs/1711.04778
publication (08/06/18), paywall https://www.nature.com/articles/s41550-018-0531-z
I'm a bit confused as to what you mean by "hit for DM". It sounds like this is a paper which suggests that the reported signal which some people thought might have been from dark matter was more likely to be associated with stars instead. To me, that doesn't say anything one way or the other about DM. It's just a bit disappointing that the nature of dark matter is proving so difficult to discern.

Mentor
2021 Award
I'm a bit confused as to what you mean by "hit for DM". It sounds like this is a paper which suggests that the reported signal which some people thought might have been from dark matter was more likely to be associated with stars instead. To me, that doesn't say anything one way or the other about DM. It's just a bit disappointing that the nature of dark matter is proving so difficult to discern.
Yes. It's just another observation which can be explained by classical results, although some have hoped to be DM radiation. Just a chance less to resolve the mystery. I admit that the authors' reference to DM is a bit artificial and feeds the suspicion that it was due to PR, as was my formulation "hit". But how ever one might look at it, it's one chance less.

There is another point in favor of something. ##\Omega=1## with ordinary matter ~ .04, the rest being dark matter ~ .25, and the bulk being dark energy.

Staff Emeritus
2021 Award
MOND theories have not done well against experimental evidence. In particular, for example, Google the "Bullet Cluster"

Bad example, despite the popular press. Abell 520 is a "reverse bullet cluster" in which the dark matter stays behind the gas, "impossible" in LCDM.

The better argument is to admit that MOND works marginally better than LCDM on galactic scales, but nowhere else.

AlenKovac
Staff Emeritus
2021 Award
Why do the images show the opposite?

Because Abell 520 and the Bullet Cluster are opposite each other in terms of the relative locations of luminous and dark matter. If your question is "why do some collisions look one way and others the other?" I don't think anyone knows. I just think one cannot say of the Bullet Cluster "This is a smoking gun - absolute irrefutable proof!" and of Abell 520, "Well you can't tell anything from one example, this is a complicated business...."

Gold Member
How certain are scientists that the solution to the dark matter problem is a new, unknown particle (or more)? Theories that eliminate the need for new particle(s) and suggest modifications to the current understanding of gravity seem to get less attention. Why is that?

I think it is always useful to focus on the consensus before leaping into the controversy. So, here are four big points.

FIRST

There is no reasonable doubt that the phenomena attributed to dark matter exist and cannot be explained with general relativity as currently formulated and the particles and forces in the Standard Model of Particle Physics alone.

This is an area of rock solid scientific consensus.

Beyond "Core Theory" (i.e. Standard Model + General Relativity) physics are necessary to explain almost all astronomy phenomena at the dwarf galaxy scale or larger. General relativity alone can explain the solar system, most of the important details about black holes, most binary star systems, and gravitational lensing and red shift, without resort to dark matter or modifications to gravity, but beyond that you need the new physics that everyone is looking for. It is a great unsolved problem.

There are other "unsolved problems" in physics like the hierarchy problem or the strong force CP problem or questions about why the initial conditions of the universe where what we have observed them to be as far back as we can measure with out available resources, that basically ask, "why are the laws of physics and its physical constants the way that they are."

But, this problem isn't in that category. Everyone agrees that we need to add new physical laws/particles/constants to existing Core Theory applied using existing methods to explain what we see.

(I say "to existing Core Theory applied using existing methods" to recognize a third possibility that could exist instead of, or in addition to the dark matter particles and modified gravity, which is that some or all of dark matter phenomena could arise from the possibility that using a Newtonian approximation of GR in lieu of complete GR to do galaxy plus scale estimates of behavior under GR could be less negligible than previously realized due to previously unrecognized flaws in how the discrepancy between a Newtonian approximation and a GR calculation is estimated. One or two people are argued this in published papers that were largely refuted, but neither side's analysis was really rigorous and extraordinarily careful so this isn't an impossibility.)

SECOND

There is no single widely accepted theory that explains all dark matter phenomena.

Dark Matter Particle Theories

Within the dark matter particle paradigm, the evidence has ruled out a lot of the potential dark matter particle parameter space. For example, both MACHOs like red dwarfs and stellar sized or larger black holes, and the hundreds of GeV WIMPs that interact via the weak force as anticipated in electroweak scale supersymmetry theories, have been all but ruled out experimentally. We know that dark matter can't be ordinary neutrinos. We know that dark matter can't be ordinary interstellar gas or planets or free neutrons.

But, we don't have positive proof for any dark matter particle candidate to the exclusion of the alternatives. And, we have multiple competing hypotheses about potential kinds of dark matter particles. Some of the hottest models are "warm dark matter", "fuzzy dark matter", "self-interacting dark matter", "sterile neutrinos", "axion-like dark matter", "mirror matter", "bosonic dark matter", etc. But, in an effort to emphasize the consensus rather than the controversy, I'm not going to carefully parse which of these models still is or is not in the running in detail in this reply.

(Note that the line between bosonic dark matter particles and a gravity modification mediated by a new fifth force carrier boson can start to overlap.)

Modified Gravity Theories

There is also no widely accepted modified gravity theory that explains all dark matter phenomena.

MOND and TeVeS

Milgrom's 1983 MOND theory is the most famous, and deservedly so. It explains the dynamics of everything from dwarf galaxies to elliptical galaxies and wide binary star systems with a single tweak to Newton's GMm/r2 law and one additional universal constant, with an accuracy as great as experimental error in the measurements that are being tested permits from ordinary matter distributions alone. It has made multiple accurate predictions in its domain of applicability that have been tested with subsequently acquired data, which no other theory has done. Also, while it underestimates dark matter phenomena in galactic clusters, it explains a significant share of the dynamics that GR does not even in those systems, and it does so without screwing up sub-galaxy scale systems like the solar system any more badly than Newtonian gravity does.

(Dirty little secret: almost all galaxy scale gravitational models that are done with general relativity are actually done with plain old Newtonian gravity anyway, because the differences between Newtonian gravity and general relativity as currently formulated and as calculated appears to be negligible in those weak fields).

But, no serious proponent of MOND has ever claimed that MOND itself is a correct theory of gravity. It is a phenomenological toy model that, at a minimum, must be correctly generalized to a relativistic version that can accurately predict things like black holes and gravitational lensing and gravitational red shift and the perihelion of Mercury and frame dragging and the like that general relativity does and Newtonian gravity does not.

MOND was generalized into relativistic form by Bekenstein into a theory known as TeVeS (for tensor, vector, scalar, in contrast to GR which is a purely tensor theory), and that solved the really glaring and obvious problems that come from generalizing Newtonian gravity rather than general relativity. But, it has not fared very well in other tests designed to discriminate between competing theories designed to explain dark matter phenomena.

Other Modified Gravity Theories

There are other modified gravity theories, such as Moffat's MOG theories (almost everyone in the field has multiple version of their theory and I use the most well known names for each) which is not only relativistic, but solves the cluster problem that MOND has, explains the Bullet Cluster, and has been explored at a cosmology level and performed reasonably well (few other modified gravity theories have been explored at this level of detail). (For what it is worth, MOG, like TeVeS is a scalar, vector, tensor theory.)

There are quite a few others, including some I am partial to, but I'm not going to bang the drum of particular little known theories in this reply.

There are another class of theories such as f(R) theories and f(T) theories and tensor-scalar theories that make tweaks to Einstein's field equations, usually adding something extra where the stress-energy tensor would ordinarily go. These have the virtue of being mathematically consistent and fully relativistic in ordinary circumstances from the get go. Initially and still predominantly now, these theories are primarily targeted at finding an alternative to the cosmological constant to explain phenomena known as "dark energy" and to probe possibilities like cosmological inflation in a more bounded manner than just coming up with ad hoc inflation theories. But, some of them can reproduce, at least, basic dark matter phenomena too.

Most of these theories are classical theories of gravity, like GR and Newtonian gravity and MOND, but a few are inspired by quantum gravity concepts. These are notable because for entirely independent and mostly theoretical reasons, we know that something in our Core Theory is wrong because the Standard Model of Particle Physics and GR are not fully compatible and we need at a minimum a quantum gravity theory to solve that disconnect, whether or not that quantum gravity theory solves any dark matter or dark energy phenomena issues. So, we really have two gravity related areas where we known to almost a certainty that we need new physics. Unfortunately, formulating a viable theory of quantum gravity is much harder than you would naively expect it to be.

Quantum gravity is mostly hard because a self-interacting spin-2 massless graviton in four dimensions does not have a rapidly converging propagator in the way that, for example, the spin-1 massless photon which is not self-interacting does. The mathematical problems with doing calculations regarding the behavior of a self-interacting spin-2 massless graviton in four dimensions are similar in kind to the mathematical problems involved in quantum chromodynamics a.k.a. QCD a.k.a. the part of the Standard Model of Particle Physics that gives rise to the strong force, but worse. QCD is slow converging but can be calculated using perturbative QCD methods similar to those of QED (the quantum version of electromagnetism) and the weak force, except at low energies, but naive quantum gravity is not renormalizable. Theorists are looking for shortcuts and unexpected symmetries that simplify these calculations.

Conventional wisdom in the quantum gravity field is that distinctions between quantum gravity and classical GR should matter most in strong field situations like near black holes and the Big Bang and at small distance scales, however, while both dark matter and dark energy phenomena, to the extent that they are gravity modifications, are instead tweaks to very weak gravitational fields (in terms of accelerations or forces) in very large systems.

One of the problems on the side of the research is that few specific theories have received enough investigation and development to rigorously test them once they clear the first hurdle of explaining the galactic rotation curves that MOND does.

THIRD

Lots of new data is coming in on all sorts of fronts on a daily basis that is useful to solving the problem of dark matter phenomena. We have direct dark matter detection experiments, experiments trying to look for dark matter particle annihilation signatures, telescopes looking as the dynamics of matter in large systems at all sorts of frequencies and with new means like neutrinos, other cosmic rays and gravitational waves, telescopes looking at the very early universe by means other than the cosmic microwave background radiation, LHC searches, etc. Some examples can be helpful to illustrate this enterprise.

Direct dark matter detection experiments and LHC searches can narrow the parameter space of any kind of dark matter particle that couples to ordinary matter or Standard Model force carrier bosons (or the Higgs boson). The null results to date of those searches imply that dark matter is either outside the range of roughly 1 GeV to 1000 GeV that has been throughly tested, or that it has very weak interactions (much weaker than neutrinos) with ordinary matter indeed. Progress is being made towards extending this exclusion range towards heavier and towards light dark matter particle mass ranges.

One important kind of observation involve the RAVE apparatus, which, among other things, makes it possible to carefully observe the dynamics of the small number of stars outside the galactic plane in the Milky Way galaxy, which in turn, allows investigators to test dark matter particle halo shapes and modified gravity models that have indistinguishable effects on the main rotation dynamics of stars in the main galactic plane of our spiral galaxy, but give rise to different gravitational fields that can be distinguished outside the plane of that disk.

CMB observations like those of the Planck collaboration and 21cm radio wave observations, that are just becoming available, probe the very early universe, in its first half-billion years or so.

Gravitational wave telescopes combined with visible light and neutrinos observations of black hole-neutron star collisions (only one so far, but soon to be many more) provide independent constraints on Hubble's Constant (which is pertinent to dark energy) and severely constrains any deviation from a massless graviton in the theory's carrier bosons (some modified gravity theories have more than one carrier boson, one or more of which may be massive).

Observations of the dynamics of very low surface brightness galaxies both near other galaxies and clusters, and in isolation, make it possible to probe whether a probe of a property of MOND all the back in 1983 that directly contradicts general relativity, called the "external field effect" does or does not exist, in a model dependent way.

This is very unlike the story in high energy particle physics, were there is basically one mega-experiment in town that can't grow in power nearly as fast as we wish it could without a big new investment of \$ that is a bottleneck on progressive on the experimental front.

In dark matter physics, in contrast, we have lots of data, we are getting more every day, we are getting more kinds of data every few years, and we are finding better and better ways to collate and analyze these various streams of data. More input is coming in faster than we can analyze it and lots of that data is evidence that will be very useful in discriminating between dark matter hypotheses.

FOURTH

On the dark matter particle paradigm side of the enterprise of explaining dark matter phenomena, it isn't good enough to come up with an answer that simply give you one or several new particles with particular properties and possibly a force or two to govern their interactions.

A dark matter particle theory needs to not only tell you what new particles and forces it needs, it needs to explain how those particles ended up in the precise places in the universe where we see them, and it needs to be capable of making precise and accurate predictions at all scales. A dark matter particle theory without an accompanying theory about the galaxy and mass assembly progress isn't much of a theory.

Most glaringly, any dark matter particle theory that doesn't modify gravity has to explain why MOND manages to explain so much, so accurately, over such a broad range of applicability, with one little tweak to Newton's theory of gravity and one universal constant. Until your dark matter particle theory can do that, it is either wrong (if it fails to reproduce this phenomenological relationship) or incomplete.

BEYOND CONSENSUS

At this juncture, the task ahead is to carefully develop the existing theories of both types that haven't been ruled out so that we know what they predict, and to continue to hypothesize and explore new alternatives to existing theories, while continually tightening the noose of the acceptable parameter spaces and necessary experimental tests that must be met by any winner.

Dark matter particle theorists and modified gravity theorists are marshaling their evidence and making their cases.

On the dark matter particle side, probably the biggest barrier to any definitive conclusion is developing better N-body simulation or analytical simulation models that show what a particular kind of dark matter particle should imply. Current simulations are tuned to post-dict what we observe with a dozen plus adjustable parameters that give the theory as tested in the simulation far more degrees of freedom than modified gravity theories have, with parameters that don't alway have great justifications from fundamental physics. Until then, it is very hard to figure out which proposals can really reproduce the galaxy scale structure and inferred dark matter halo shapes that we infer from dynamics. When there isn't a match, we don't know if the simulation is broken or the hypothesis is wrong. When there is a match, we don't know if this is really an artifact of excessive tuning in our simulation, or if the theory is actually correct.

On the modified gravity side, one of the biggest barriers is to find the resources to examine questions like what theories predict about the state of the early universe. Dark matter particle theorists point to the LamdaCDM "Standard Model of Cosmology's great success at explaining the cosmic background radiation and other much larger than galactic cluster scale features of the universe. But, often in the case of modified gravity theories, the problem isn't that the theories contradict the Standard Model of Cosmology, but that it is much harder to tell how the non-linearities in these modified gravity theories change the predictions for the early universe. Simply put, nobody has really gotten around to that rigorously for many of the most promising modified gravity theories.

Still, this is a problem that honestly could have an evidence based solution in decades and not centuries. You have a good shot of living to hear the final consensus.

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Klystron, Buzz Bloom, Buckethead and 4 others
Gold Member
Bad example, despite the popular press. Abell 520 is a "reverse bullet cluster" in which the dark matter stays behind the gas, "impossible" in LCDM.

The better argument is to admit that MOND works marginally better than LCDM on galactic scales, but nowhere else.
This kind of thing doesn't really overturn the bullet cluster result at all. Nor does it argue against dark matter in favor of modified gravity. In a universe where dark matter exists alongside baryonic matter like our own, you expect there to be really complicated stuff that happens. The Bullet Cluster is a nice test because it is a relatively clean system: it is a system where a comparatively smaller galaxy cluster rammed through a larger galaxy cluster at high velocity. The simplicity of the Bullet Cluster makes it incredibly difficult to explain in any modified gravity model (the one example I'm aware of that comes close introduces its own, novel form of dark matter, a heavy neutrino).

Abell 520, sometimes called the Train Wreck Cluster, is a vastly more complicated system which apparently formed at the crossing of three filaments of large-scale structure. This far more complex structure will naturally be more challenging to understand in detail. It's trivially easy to understand how such a structure might have a dark core (such dark cores will naturally form at the intersections of filaments). What's more confusing is why that dark core has so few galaxies in it: you'd generally expect that large concentrations of dark matter should coincide with very massive galaxies.

Claiming that it argues against dark matter makes no sense whatsoever. It's rather like the argument that global warming is false because some places still get unseasonably cold in winter. A universe where the "missing mass" is explained by modified gravity has no mechanism whatsoever for there to be different amounts of dark matter vs. normal matter in different systems. A universe with dark matter has lots of potential mechanisms for this to happen.

How certain are scientists that the solution to the dark matter problem is a new, unknown particle (or more)? Theories that eliminate the need for new particle(s) and suggest modifications to the current understanding of gravity seem to get less attention. Why is that?

The short answer is it depends who you talk to. Some astronomers are very convinced about dark matter others not so. In the absence of a definite dark matter candidate the debate will continue. Possibly, the dark matter group just edge this with popularity and not forgetting many have spent a lot of money and long careers looking for dark matter!

Gold Member
Modified theories of gravity have gotten a lot of attention, and continue to do so. But most cosmologists think they're highly unlikely at this point because the evidence just doesn't point that way. Still, these kinds of theories have a certain kind of allure to many theorists, so there continues to be work in modified gravity theories to attempt to explain dark matter (and dark energy).

I would disagree with your assessment about which way the evidence points, although in fairness, some of the strongest reasons to disagree involve quite recent evidence.

One of the biggest involves dark matter particle parameter space. LambdaCDM isn't very demanding when it comes to dark matter candidates. They need to have 10eV/c2 or more of mass, it needs a density the declines proportionately to the expanding volume of the universe, and it needs to be "nearly collissionless" an approximation that isn't very exacting when you get down to brass tacks.

Truly collisionless dark matter is easy to model. It forms halos that fit what is called an NFW profile (after the initials of the people who came up with it). But, recent observations pretty conclusively establish that inferred dark matter halos do not fit the NFW profile. And, equally important, it doesn't tightly, tightly align itself with the distribution of ordinary matter. Gravity causes the two to mutually influence the halo and ordinary matter distributions, but it shouldn't do so that strongly in a wide variety of galaxy systems. For example, if dark matter is truly collisionless, galaxies with bulges should have quite different halos from galaxies without them, even though they have quite similar rotational dynamics. You can tweak the NFW profile a bit by reducing the mass of the dark matter particles to the keV mass range, because some quantum effects start to kick in at that point, but it really isn't enough to reproduce observation (the lower mass of the dark matter particles also increases their anticipated average velocity which helps solve the fact that the amount of satellite galaxy and subhalo structure predicted for heavier dark matter particles that move more slowly is not observed). Truly collisionless dark matter is also a very bad fit to the 21cm radio wave observations of the early universe, that need dark matter to cool radiation era energy.

But, if you have strong enough cross-sections of interaction to solve the problems with a truly collisionless model, by creating some sort of weak feedback between dark matter and ordinary matter, you start to screw up the CMB predictions that are the crowning achievement of LambdaCDM, although this could explain why galaxy formation observations seem to point to this happening earlier than predicted in a plain vanilla LambdaCDM scenario (something that also happens in the couple of modified gravity theories whose cosmologies have been explored more rigorously). The stronger the cross-section of interaction you have, the more of a problem the null results from the direct detection experiments and the LHC become as well.

Apparent observations of the external field effect in the Crater II galaxy, and apparent MOND-like behavior in wide binary stars, are two more very convincing pieces of evidence in support of modified gravity theories that are both completely inconsistent with dark matter halo theories. The former contradicts GR, which no dark matter particle theory can do without a fifth forth of a kind that hasn't been well formulated at this point in the dark matter particle context. It is extremely hard to model that later effect through a dark matter halo.

[Note to mods - I'll try to sprinkle in some citations soon, there are papers for everything that I have indexed links to, but I'm a work and have already spent way too much time on physics today, so I've got to go. I'll also try to go back for some copy editing.]

Gold Member
I would disagree with your assessment about which way the evidence points, although in fairness, some of the strongest reasons to disagree involve quite recent evidence.

One of the biggest involves dark matter particle parameter space. LambdaCDM isn't very demanding when it comes to dark matter candidates. They need to have 10eV/c2 or more of mass, it needs a density the declines proportionately to the expanding volume of the universe, and it needs to be "nearly collissionless" an approximation that isn't very exacting when you get down to brass tacks.

Truly collisionless dark matter is easy to model. It forms halos that fit what is called an NFW profile (after the initials of the people who came up with it). But, recent observations pretty conclusively establish that inferred dark matter halos do not fit the NFW profile. And, equally important, it doesn't tightly, tightly align itself with the distribution of ordinary matter. Gravity causes the two to mutually influence the halo and ordinary matter distributions, but it shouldn't do so that strongly in a wide variety of galaxy systems. For example, if dark matter is truly collisionless, galaxies with bulges should have quite different halos from galaxies without them, even though they have quite similar rotational dynamics. You can tweak the NFW profile a bit by reducing the mass of the dark matter particles to the keV mass range, because some quantum effects start to kick in at that point, but it really isn't enough to reproduce observation (the lower mass of the dark matter particles also increases their anticipated average velocity which helps solve the fact that the amount of satellite galaxy and subhalo structure predicted for heavier dark matter particles that move more slowly is not observed). Truly collisionless dark matter is also a very bad fit to the 21cm radio wave observations of the early universe, that need dark matter to cool radiation era energy.

But, if you have strong enough cross-sections of interaction to solve the problems with a truly collisionless model, by creating some sort of weak feedback between dark matter and ordinary matter, you start to screw up the CMB predictions that are the crowning achievement of LambdaCDM, although this could explain why galaxy formation observations seem to point to this happening earlier than predicted in a plain vanilla LambdaCDM scenario (something that also happens in the couple of modified gravity theories whose cosmologies have been explored more rigorously). The stronger the cross-section of interaction you have, the more of a problem the null results from the direct detection experiments and the LHC become as well.

Apparent observations of the external field effect in the Crater II galaxy, and apparent MOND-like behavior in wide binary stars, are two more very convincing pieces of evidence in support of modified gravity theories that are both completely inconsistent with dark matter halo theories. The former contradicts GR, which no dark matter particle theory can do without a fifth forth of a kind that hasn't been well formulated at this point in the dark matter particle context. It is extremely hard to model that later effect through a dark matter halo.

[Note to mods - I'll try to sprinkle in some citations soon, there are papers for everything that I have indexed links to, but I'm a work and have already spent way too much time on physics today, so I've got to go. I'll also try to go back for some copy editing.]
Missing from this are two important facts:
1. Modified gravity models have so far utterly failed to explain the CMB data (here's one formal argument along these lines from 2011, which I'm pretty sure remains valid to this day: https://arxiv.org/pdf/1112.1320.pdf).
2. The above argument asks you to disregard observations of comparatively simple systems (e.g. the CMB) and instead focus on comparatively complex systems (e.g. galaxies). Systematic uncertainties are far, far more likely to muddle our understanding of complex systems.

PeterDonis
Staff Emeritus
2021 Award
This kind of thing doesn't really overturn the bullet cluster result at all.

I'm not saying it does. I am saying that a single observation (in this case the Bullet Cluster) is not nearly as simple and as unambiguous as the popular press (and some astronomers) make it out to be.

ohwilleke
Gold Member
I'm not saying it does. I am saying that a single observation (in this case the Bullet Cluster) is not nearly as simple and as unambiguous as the popular press (and some astronomers) make it out to be.
The Bullet Cluster result remains quite striking, due to the relative simplicity of its structure. There are many other systems which are more difficult to understand.

But I still think the CMB is vastly stronger evidence for dark matter. The Bullet Cluster's main points in its favor are that it's easy to explain and has some pretty pictures associated. Even though its structure is relatively simple, any galaxy cluster will remain pretty complicated.

But with the CMB, the physics involved are tremendously better-understood than the physics responsible for the formation and behavior of galaxies and galaxy clusters. The fundamental quality that makes the CMB so easy to deal with is that the CMB was emitted long before most of the matter in the universe collapsed into dense configurations (e.g. galaxy clusters). The smoothness of the universe when the CMB was emitted makes it so that linearized gravity is an excellent approximation. With the ability to use linearized gravity, it's possible to calculate very precisely the behavior of the early-universe fluid given the physical properties of that fluid.

This contrasts with the formation of galaxy clusters and galaxies, where many of the calculations are simply impossible to do in an exact manner. We have to instead use approximations such as N-body simulations to attempt to determine their behavior over time. To get a rough idea of how much easier it is to calculate things using the CMB, it's possible with a modern desktop computer to calculate the power spectrum given a model of the universe within seconds. N-body simulations generally still require large clusters to run the simulations over an extended period of time. There are ways to make approximate calculations for large-scale structure which take less time, but they always sacrifice significant accuracy.

Buzz Bloom
Bad example, despite the popular press. Abell 520 is a "reverse bullet cluster" in which the dark matter stays behind the gas, "impossible" in LCDM.
Isn't the train wreck cluster still evidence for DM, or at the very least - against modified gravity, though?
Both here and with the bullet cluster, or any other cluster where the source of gravity is seen separate from matter, there has to be something extra there that sources gravity. Something not collocated with visible matter - i.e., it can't be a modification of gravity sourced by that visible matter only.
How did the two sources get apart this way or the other is a secondary question.

Staff Emeritus
2021 Award
If you take Abell 520 as it appears, it tells you that DM clumps more than ordinary matter. If you take the Bullet Cluster as it appears, it tells you DM clumps less than ordinary matter. Both cannot be true.

Kimbyd argued that we should ascribe more weight to the Bullet Cluster, since it's simpler. I don't agree with her. I believe that neither system is simple. For example, the Bullet Cluster's velocity is higher than comfortable for LCDM.

Kimbyd argued that we should ascribe more weight to the Bullet Cluster, since it's simpler. I don't agree with her. I believe that neither system is simple. For example, the Bullet Cluster's velocity is higher than comfortable for LCDM.
I'll quote @Wallace from another thread, when Abell 520 was first (?) discussed here:
The nice thing about the Bullet Cluster is that we are lucky in that we see the collision almost perfectly edge on, and that the two clusters involved were both spherical, relaxed clusters without significant substructure, they were of similiar mass, and we see the collision on the 'first pass'. All of this means that quite simple modes for the clusters (in terms of the radial density profiles etc) are good approximations, making the modelling relatively straight forward.

Abell 520 is, on the other hand, a complete mess, with all kinds of sub-structure and the fact that we are seeing a merger that has been going on for a while, rather than the first pass of two clusters. This makes the modelling tricky and the results unclear. It just means that the Bullet Cluster is a nice clean 'lab' for testing DM and gravity while Abell 520 is a lot messier, for whatever theory you are considering.
I'm pretty sure that's the kind of simplicity that was being talked about. It's just simpler to model.

Other than that, I think we all agree that the Bullet Cluster shouldn't be treated as a *cough* silver bullet of DM search.

Marisa5 and ohwilleke
Gold Member
If you take Abell 520 as it appears, it tells you that DM clumps more than ordinary matter. If you take the Bullet Cluster as it appears, it tells you DM clumps less than ordinary matter. Both cannot be true.
1. The mass of Abell 520 is more spread-out than the normal matter (which is mostly made up by the hot cluster gas), so your first statement is flat wrong.
2. Neither of these two conclusions is really relevant to the argument at hand.

Kimbyd argued that we should ascribe more weight to the Bullet Cluster, since it's simpler. I don't agree with her. I believe that neither system is simple. For example, the Bullet Cluster's velocity is higher than comfortable for LCDM.
1. The high velocity is utterly irrelevant to the structure of the cluster: it's more an external, theoretical constraint. It has no bearing on the statement that the Bullet Cluster is a relatively simple system.
2. The CMB is far, far simpler still. If you're not starting with CMB data in discussions on dark matter, you're not presenting a good argument.

Gold Member
Missing from this are two important facts:
1. Modified gravity models have so far utterly failed to explain the CMB data (here's one formal argument along these lines from 2011, which I'm pretty sure remains valid to this day: https://arxiv.org/pdf/1112.1320.pdf).

As I note above in my earlier post on this thread, this is mostly because nobody has worked out what more than one or two Modified gravity models predict the CMB data to be. Whether or not they are consistent or inconsistent with the CMB data is an open question.

My intuition is that modified gravity effects that are difficult to distinguish from dark matter particles in other contexts, such as galaxy dynamics, are likely to also be difficult to distinguish from dark matter particles in the CMB context once you properly do the analysis of what modified gravity theories predict for that.

2. The above argument asks you to disregard observations of comparatively simple systems (e.g. the CMB) and instead focus on comparatively complex systems (e.g. galaxies). Systematic uncertainties are far, far more likely to muddle our understanding of complex systems.

The CMB is not meaningfully more simple than galaxies. There are plenty of potential systemic uncertainties in both systems, indeed to potential uncontrolled systemic uncertainties in the CMB data are quite a bit greater because we can directly observe galaxies with many examples, allowing us to rule out or limit systemic uncertainties, while the singular CMB event is one in which we have to rely much more heavily upon assumptions. Those assumptions, by and large, turn out to be O.K. which is why LambdaCDM can work. But, that isn't a reason to prefer one over the other by itself.

Also naive LambdaCDM with true collisionless cold dark matter fails spectacularly in every context other than the CMB and dark energy, and is starting to show inconsistencies even on the cosmology front with issues like the impossible early galaxy problem and the 21cm observations, so it isn't as convincing as it might be. The mechanism LambdaCDM assumes to produce this model's results is highly problematic when compared to all of the evidence, even though the model works to predict what it is designed to predict.

Gold Member
As I note above in my earlier post on this thread, this is mostly because nobody has worked out what more than one or two Modified gravity models predict the CMB data to be. Whether or not they are consistent or inconsistent with the CMB data is an open question.

My intuition is that modified gravity effects that are difficult to distinguish from dark matter particles in other contexts, such as galaxy dynamics, are likely to also be difficult to distinguish from dark matter particles in the CMB context once you properly do the analysis of what modified gravity theories predict for that.
Okay. But none of that matters unless the work is actually done. I, for one, think your intuition is completely wrong. In large part because dark matter theories generally don't do well at explaining both galaxies and galaxy cluster dynamics at the same time (they typically have an exceptionally difficult time with galaxy clusters).

I get that doing sound wave simulations in linearized gravity can be a daunting task. But the high-quality nature of the data set demands it. Until dark matter theorists demonstrate this, not just at a surface level but in detail, I see no point in even entertaining their theories.

The CMB is not meaningfully more simple than galaxies.
It is overwhelmingly more simple. The comparison isn't even remotely close. Galaxy dynamics still has lots and lots of huge unknowns that have dramatic consequences for their overall properties. Here are a few of the ways in which the CMB is simpler:
1. Gravity dynamics are simple. The density contrast at work during the CMB allows the use of linearized gravity, which allows simulations with minimal approximations to go from the inflationary era all the way forward to the emission of the CMB with a few seconds of computing power. To do anything remotely similar with galaxies, you have to use N-body simulations.
2. No relevant compact objects. While primordial black holes remain an exotic possibility, we do know that they can't impact the CMB signal by very much if they exist at all. Galaxies have very complex interrelationships between supernovae, gas and dust in the galaxy, and the supermassive black holes at their centers. None of that happens in the pre-CMB universe: you just have a nearly-uniform plasma with sound waves.
3. All of the normal matter is visible. With galaxies, not everything is bright. And even the parts that are bright might be too dim for a given observation. So even absent dark matter, much of the normal matter presence must be implied rather than directly-measured. With the CMB, we see all of the normal matter that existed at the time.
4. The initial conditions are extremely well-controlled. The models which match the CMB well use very simple stochastic processes to lay down the initial conditions for CMB simulations. To date, there has been no deviation from these stochastic initial conditions which has been unambiguously detected. For galaxies, often times we don't even know the right initial conditions to use because each individual galaxy will tend to have a complex formation history, complete with large numbers of mergers.

I don't even know how you can even begin to claim that the two systems are anywhere in the same regime of observational simplicity. There are a lot of systematic uncertainties with the CMB, but they're at the level of tweaking some of the worse-measured parameters. The dark matter abundance, by the way, is one of the best-measured parameters for the CMB (specifically, the ratio of dark matter to normal matter is extremely well-measured). The main systematic uncertainties with respect to the CMB are related to polarization measurements, and the dark matter signal doesn't rely on those measurements at all.

There are plenty of potential systemic uncertainties in both systems, indeed to potential uncontrolled systemic uncertainties in the CMB data are quite a bit greater because we can directly observe galaxies with many examples,
The CMB is observed over the entire sky, with modern measurements obtaining accurate temperature data in millions of independent pixels. The number of samples for the CMB data set is not limited in the least.

Also naive LambdaCDM with true collisionless cold dark matter fails spectacularly in every context other than the CMB and dark energy
A) There's no truth to that statement. At worst there's a mismatch in the most dense regions between naive ##\Lambda##CDM and observations. But that mismatch is not dramatic compared to the measurement uncertainties in play.
B) Collisionless dark matter is generally not considered to be the most likely anyway.

Gold Member
A) There's no truth to that statement. At worst there's a mismatch in the most dense regions between naive ##\Lambda##CDM and observations. But that mismatch is not dramatic compared to the measurement uncertainties in play.
B) Collisionless dark matter is generally not considered to be the most likely anyway.

But, the third peak in the CDM is largely a consequence of the hypothesis that dark matter is collisionless, so if the strongest evidence for the DM paradigm is the LambdaCDM paradigm (and on that point I tend to agree with you), then non-collisionless dark matter hypotheses are really serious problem with the model.

A summary of the small scale problems with LambdaCDM from an author who just a few weeks ago wrote a controversial paper claiming that the alleged universal acceleration scale of MOND doesn't exist (i.e. a modified gravity skeptic) explains this in the follow, understated, abstract:

The ΛCDM model, or concordance cosmology, as it is often called, is a paradigm at its maturity. It is clearly able to describe the universe at large scale, even if some issues remain open, such as the cosmological constant problem , the small-scale problems in galaxy formation, or the unexplained anomalies in the CMB. ΛCDM clearly shows difficulty at small scales, which could be related to our scant understanding, from the nature of dark matter to that of gravity; or to the role of baryon physics, which is not well understood and implemented in simulation codes or in semi-analytic models. At this stage, it is of fundamental importance to understand whether the problems encountered by the ΛDCM model are a sign of its limits or a sign of our failures in getting the finer details right. In the present paper, we will review the small-scale problems of the ΛCDM model, and we will discuss the proposed solutions and to what extent they are able to give us a theory accurately describing the phenomena in the complete range of scale of the observed universe.

The introduction is a good summary of the conceded problems with LambdaCDM from the perspective of a modified gravity skeptic, and I will quote it at length:

Despite the ΛCDM model being successful, according to the largest part of the cosmology community, in describing the formation and evolution of the large scale structure in the Universe, the state of the early Universe and the abundance of different forms of matter and energy [1–5], its predictive power — already checked against new discoveries (e.g., lensing of the CMB [6,7], B-mode polarisation [8] the kinetic SZ effect) — it presents several difficulties. Among the most famous, we recall the “cosmological constant fine tuning problem”, and the “cosmic coincidence problem” [9,10].

The first problem is connected to the fact that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum at present, more than 100 orders of magnitude too large, see Refs. [9–11]. More precisely the theoretical expectations give ρΛ ' 1071 GeV4 , in contradiction with the cosmological upper bounds giving ρΛ ' 10−47 GeV4 which gives rise to an extreme fine-tuning problem. It also entails fine tuning at Planck scale era, thus in the initial conditions of dark energy. The second is connected to the reason why dark energy and dark matter energy densities are approximately equal nowadays (see Ref. [12]).

Tensions of unknown origin are also present between the 2013 Planck parameters [13] and σ8 obtained from cluster number counts and weak lensing, the actual value of the Hubble parameter, H0, and SN IA data. The Planck 2015 data are still in tension with CFHTLenS weak lensing [14] data, and with the σ8 growth rate [15].

Another concern lies in that the large-angle fluctuations in the CMB show statistical anomalies (i.e., a quadrupole-octupole alignment [16–20], a power hemispherical asymmetry [21–26] and a cold spot [27–29]). This collides with the idea that our universe should be a realisation of a statistically isotropic and Gaussian random field, which implies a statistical independence in the CMB multipoles. What is unclear is whether these anomalies are related to unknown systematics, if they are statistical effects [30], or a fingerprints of new physics.

The ΛCDM model also encounters problems in describing structures at small scales, e.g., [31–36]. The main problems are/have been

a. The cusp/core (CC) problem [31,37], designating the discrepancy between the flat density profiles of dwarf galaxies (also coined dwarfs), Irregulars, and Low Surface Brightness galaxies (hereafter LSBs), and the cuspy profile predicted by dissipationless N-body simulations [38–40], despite the fact that the observed galaxies are all of DM dominated types;

b. The “missing satellite problem” (MSP), coining the discrepancy between the number of predicted subhalos in N-body simulations [32,41] and those actually observed, further complicated by the “Too Big To Fail” (TBTF) problem, arising from the ΛCDM prediction of satellites that are too massive and too dense, compared to those observed, to hope for their destruction in the history of mass assembly up to today [34,35];

c. The angular momentum catastrophe [42] labelling the angular momentum loss in Smooth Particle Hydrodynamics (SPH) simulations of galaxy formation that gives rise to dwarf galaxies’ disks with different angular momentum distributions from those of cold dark matter haloes, in addition to disc sizes that are much smaller in simulated galaxies compared with observed ones [43];

d. The problem of satellites planes, namely the alignment on thin planes of satellite galaxies of the MW and M31, a feature that proved difficult to explain in simulations of the ΛCDM paradigm [44];

e. The problem of re-obtaining the slope and scatter of the baryonic Tully-Fisher relation (Mb ∝ V 4 c ) [45];

The ΛCDM model has some other issues discussed in Refs. [46–50], that we shall not consider in our short review.

Problems c and e have actually been solved: baryonic models, as discussed in Section 4.1, have already been proposed to solve the problem posed by SPH simulations baryons angular momentum non conservation in collapse, leading them to typically only retain 10%, and form disks that are too small, compared to real galaxies [51–54] (i.e., the “angular momentum catastrophe”, AMC). Those solutions proceeded from feedback effects basically heating the gas , from supernovae explosions [53], using clumps, in addition, to reproduce the correct angular momentum distribution of baryons [55–57] and selective outflows to obtain bulgeless disks [58] (see Section 4.2), or from dynamical friction of baryonic clumps, able to explain all those features at once (see Section 4.3, and Ref. [59]).

The empirical optical luminosity-21 cm line width scaling in spiral galaxies, the Tully-Fisher relation [60], that reflects the gas+luminous mass-rotation velocity scaling, the Baryonic Tully-Fisher Relation (BTFR) [61–69], have been used as a stumbling stone for the ΛCDM model by proponents of the MOND Modified Gravity Model ([70], discussed in Section 4.4). However, this claim is less strong after some models and simulations have found a possible solution (see Section 3).

Problem d is characterised in the MW by
• a highly flattened, planar distribution of the satellites in three-dimensional space,
• a common orientation of the satellites orbits, and
• an alignment of the satellites orbits within the distribution plane.

and remains open: if Ref. [71] claimed a resolution in the EAGLE hydrodynamical simulations, the review [72] concluded oppositely.

The present review will be restricted to the small-scale problems of the ΛCDM model (hereafter SSPΛCDM) connected to the formation of cusps, and to satellites. As we will see hereafter, these issues are strictly connected.

From one side, unified models have shown [59,73,74] that a mechanism which can transform cusps into cores conversely helps the solution of the MSP. Several authors (e.g., [75–77]) noticed that the effects of a parent halo’s tidal forces on a satellite depend fundamentally on the shape of the latter. A cuspy profile allows the satellite to retain most of its structure, when entering the main halo. Inversely, for a cored profile, the tidal field of the main halo can easily strip the satellite from its gas and even destroy it in some cases [77]. As a result, such satellite will not end up visible, either because it was destroyed or because it lacks the gas to make stars.

From the other side, the satellites most puzzling issue is now recognised as having shifted: rather than the number of satellites, it is related to their inner mass density, specifically to their density profiles being flatter than those of N-body simulations.

For what it is worth, I've seen papers looking at problem e (the Tully-Fischer relationship) and would not at all agree that they solve that problem as claimed. The most successful recent efforts to reproduce the baryonic Tully-Fischer relation with CDM models is L.V. Sales, et al., "The low-mass end of the baryonic Tully-Fisher relation" (February 5, 2016). It explains:

[T]he literature is littered with failed attempts to reproduce the Tully-Fisher relation in a cold dark matter-dominated universe. Direct galaxy formation simulations,for example, have for many years consistently produced galaxies so massive and compact that their rotation curves were steeply declining and, generally, a poor match to observation. Even semi-analytic models, where galaxy masses and sizes can be adjusted to match observation, have had difficulty reproducing the Tully-Fisher relation, typically predicting velocities at given mass that are significantly higher than observed unless somewhat arbitrary adjustments are made to the response of the dark halo.

The paper manages to simulate the Tully-Fisher relation only with a model that has sixteen parameters carefully "calibrated to match the observed galaxy stellar mass function and the sizes of galaxies at z = 0" and "chosen to resemble the surroundings of the Local Group of Galaxies", however, and still struggles to reproduce the one parameter fits of the MOND toy-model from three decades ago. Any data set can be described by almost any model so long as it has enough adjustable parameters.

As this paper illustrates, much of the improvement over prior models has come from efforts to incorporate feedback between baryonic and dark matter into the models, but this has generally been done in a manner than is more ad hoc than it is firmly rooted in rigorous theory or empirical observations of the feedback processes in action.

The tight fit is also problematic for a theoretical reason. One of the more intractable problems with simulations based upon a dark matter particle model that has been pointed out, for example, in Alyson M. Brooks, Charlotte R. Christensen, "Bulge Formation via Mergers in Cosmological Simulations" (12 Nov 2015) is that their galaxy and mass assembly model dramatically understates the proportion of spiral galaxies in the real world which are bulgeless, which is an inherent difficulty with the process by which dark matter and baryonic matter proportions are correlated in dark matter particle models which are not a problem for modified gravity models. They note that:

[W]e also demonstrate that it is very difficult for current stellar feedback models to reproduce the small bulges observed in more massive disk galaxies like the Milky Way. We argue that feedback models need to be improved, or an additional source of feedback such as AGN is necessary to generate the required outflows.

There are also some other issues that aren't addressed, such as wide binaries and globular clusters and elliptical galaxies with planetary nebulae, and observational evidence of an external field effect in Crater II (which in fairness, he couldn't have known about in 2016):

Re Wide Binaries:

The wide binary systems are notable because it is extremely hard to explain these dynamics with particle dark matter. No one expects pairs of widely separated stars that rotate each other to have their own dark matter subhalo.

Assuming Newton's gravity and GR to be valid at all scales leads to the dark matter hypothesis as a requirement demanded by the observed dynamics and measured baryonic content at galactic and extragalactic scales. Alternatively, modified gravity scenarios where a change of regime appears at acceleration scales a<a0 have been proposed. This modified regime at a<a0 will generically be characterised by equilibrium velocities which become independent of distance. Here we identify a critical test in this debate and we propose its application to samples of wide binary stars. Since for 1M⊙ systems the acceleration drops below a0 at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching 104 AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same a<a0acceleration regime. Our results are suggestive of a breakdown of Kepler's third law beyond a≈a0 scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.

Hernandez et al., "Wide binaries as a critical test for Gravity theories" (2012) https://arxiv.org/abs/1205.5767. A November 2016 paper by Scarpa, et al., updates this result on wide binaries.

Re Globular Clusters:

Globular clusters at the fringe of a system are another place where dark matter particles are not expected to be present.

Non-baryonic Dark Matter (DM) appears in galaxies and other cosmic structures when and only when the acceleration of gravity, as computed considering only baryons, goes below a well defined value a0=1.2e-8 cm/s/s. This might indicate a breakdown of Newton's law of gravity (or inertia) below a0, an acceleration smaller than the smallest probed in the solar system. It is therefore important to verify whether Newton's law of gravity holds in this regime of accelerations. In order to do this, one has to study the dynamics of objects that do not contain significant amounts of DM and therefore should follow Newton's prediction for whatever small accelerations. Globular clusters are believed, even by strong supporters of DM, to contain negligible amounts of DM and therefore are ideal for testing Newtonian dynamics in the low acceleration limit. Here, we discuss the status of an ongoing program aimed to do this test. Compared to other studies of globular clusters, the novelty is that we trace the velocity dispersion profile of globular clusters far enough from the center to probe gravitational accelerations well below a0. In all three clusters studied so far the velocity dispersion is found to remain constant at large radii rather than follow the Keplerian falloff. On average, the flattening occurs at the radius where the cluster internal acceleration of gravity is 1.8+-0.4 x 10^{-8} cm/s/s, fully consistent with MOND predictions.

Scarpa et al., "Globular Clusters as a Test for Gravity in the Weak Acceleration Regime (2006) https://arxiv.org/abs/astro-ph/0601581. There is also a more recent August 2010 paper and a more recent September 2016 globular cluster paper by some of the same authors.

Re Elliptical Galaxies with Planetary Nebulae:

A similar observation is made regarding planetary nebula rotating around elliptical galaxies, which generaly have little dark matter relative to luminous matter in dark matter particle paradigms:

The dynamics of an elliptical galaxy within a couple of effective radii can be probed effectively by stars. However, at larger distances planetary nebulae (PNe) replace stars as the tracer of the dynamics. Making use of the motion of PNe, Romanowsky et al. (2003) measured the dynamics of three luminous elliptical galaxies (NGC821, NGC3379, and NGC4494) at large distances from the galactic center. They found that little dark matter is needed up to 6 effective radii. Milgrom & Sanders (2003) showed that this result can be understood in the framework of MOdified Newtonian Dynamics (MOND). As more data are available in the past decade, we revisit this problem. We combine PNe data (up to 6{8 effective radii) and stellar data from SAURON of 7 elliptical galaxies, including those 3 galaxies in Romanowsky et al. (2003) with updated data and 4 other galaxies which have not been analyzed before. We conclude that the dynamics of these galaxies can be well explained by MOND.

Yong Tian, Chung-Ming Ko, Dynamics of Elliptical Galaxies with Planetary Nebulae in Modified Newtonian Dynamics (Submitted on 22 Jun 2016 (v1), last revised 13 Jul 2016 (this version, v2)).

Re Crater II:

Crater II is an unusual object among the dwarf satellite galaxies of the Local Group in that it has a very large size for its small luminosity. This provides a strong test of MOND, as Crater II should be in the deep MOND regime (gin≈34km2s−2kpc−1≪a0=3700km2s−2kpc−1). Despite its great distance (≈120 kpc) from the Milky Way, the external field of the host (gex≈282km2s−2kpc−1) comfortably exceeds the internal field. Consequently, Crater II should be subject to the external field effect, a feature unique to MOND. This leads to the prediction of a very low velocity dispersion: σefe=2.1+0.9−0.6kms−1.

Stacy S. McGaugh, "MOND Prediction for the Velocity Dispersion of the `Feeble Giant' Crater II" (November 3, 2016).

This is a big deal because under a wide range of dark matter hypotheses, the velocity dispersion could have been no lower than 5 km/s and was expected to be more like 11 km/s to 24 km/s. The actual velocity dispersion of Crater II was measured with the latest and greatest telescopes in a result first announced six and a half weeks after this prediction was made on December 19, 2016. What did they find?

A velocity dispersion of 2.4 km/s to 3.0 km/s.

A variety of data on the early universe are also problem for LambdaCDM, which predicts, generally, a too slow development of various structures, indicating that something it assumes is wrong.

Black holes get too big too fast relative to its predictions:

See, Y. Kim et al. The Infrared Medium-Deep Survey. IV. Low Eddington ratio of a faint quasar at z~6: Not every supermassive black hole is growing fast in the early universe. arXiv:1802.02782v1. Posted February 9, 2018; T.C.N. Boekholt et al. Formation of massive seed black holes via collisions and accretion. Monthly Notices of the Royal Astronomical Society. Vol. 476, May 2018, p. 366. doi:10.1093/mnras/sty208; F. Pacucci et al. Conditions for optimal growth of black hole seeds. The Astrophysical Journal Letters. Published online December 1, 2017. doi:10.3857/2041-8213/aa9aea; C. Mazzucchelli et al. Physical properties of 15 quasars at z>6.5. The Astrophysical Journal. Published online November 10, 2017. doi:10.3847/1538-4357/aa9185; P. Natarajan et al. Unveiling the first black holes with JWST: Multi-wavelength spectral predictions. The Astrophysical Journal. Published online April 1, 2017. doi:10.3847/1538-4357/aa6330.

The 21cm data is a poor fit:

The profile is largely consistent with expectations for the 21-centimetre signal induced by early stars; however, the best-fitting amplitude of the profile is more than a factor of two greater than the largest predictions.

This discrepancy suggests that either the primordial gas was much colder than expected or the background radiation temperature was hotter than expected. Astrophysical phenomena (such as radiation from stars and stellar remnants) are unlikely to account for this discrepancy; of the proposed extensions to the standard model of cosmology and particle physics, only cooling of the gas as a result of interactions between dark matter and baryons seems to explain the observed amplitude. The low-frequency edge of the observed profile indicates that stars existed and had produced a background of Lyman-α photons by 180 million years after the Big Bang. The high-frequency edge indicates that the gas was heated to above the radiation temperature less than 100 million years later.

From Nature.

The 21cm data are a perfect fit, however, to a scenario with no dark matter. And, this is notable because the 21cm data are independent of other tests, because the 21cm data is measuring the thermal properties of the early universe, while almost all of the other tests are measuring the dynamics of the early galaxy in some manner or another.

A modified gravity theory retains the thermal properties of ordinary matter, while having very different dynamics.

The Impossible Early Galaxy Problem:

To understand the formation and evolution of galaxies at redshifts z < 10, one must invariably introduce specific models (e.g., for the star formation) in order to fully interpret the data. Unfortunately, this tends to render the analysis compliant to the theory and its assumptions, so consensus is still somewhat elusive.

Nonetheless, the surprisingly early appearance of massive galaxies challenges the standard model, and the halo mass function estimated from galaxy surveys at z > 4 appears to be inconsistent with the predictions of LCDM, giving rise to what has been termed "The Impossibly Early Galaxy Problem" by some workers in the field. A simple resolution to this question may not be forthcoming.

The situation with the halos themselves, however, is more straightforward and, in this paper, we use linear perturbation theory to derive the halo mass function over the redshift range z < 10 for the R_h=ct universe. We use this predicted halo distribution to demonstrate that both its dependence on mass and its very weak dependence on redshift are compatible with the data.

The difficulties with LCDM may eventually be overcome with refinements to the underlying theory of star formation and galaxy evolution within the halos. For now, however, we demonstrate that the unexpected early formation of structure may also simply be due to an incorrect choice of the cosmology, rather than to yet unknown astrophysical issues associated with the condensation of mass fluctuations and subsequent galaxy formation.

Manoj K. Yennapureddy, Fulvio Melia, "A Cosmological Solution to the Impossibly Early Galaxy Problem" (March 19, 2018).

Unexpected metal enrichment rates in early galaxies:

"If you extrapolate what is known in the local Universe, you would have expected a higher metallicity in less active star-forming galaxies than they found," said Hien Tran, staff astronomer at Keck Observatory who was not part of the finding. "It's part of the normal stellar and galaxy evolution. Onodera's team realized the role of star formation is not as strong at great distances as it is at zero. Understanding the interplay between metallicity, star formation rates and the mass of star forming galaxies will help us better understand galaxy evolution."

Because the team did not see any influence of the strength of star formation in the metal enrichment in distant galaxies, it is telling that the physical condition regulating star formation in galaxies in the early Universe is possibly different from that seen in the present-day Universe.

See M. Onodera et al. ISM EXCITATION AND METALLICITY OF STAR-FORMING GALAXIES AT ≃ 3.3 FROM NEAR-IR SPECTROSCOPY , The Astrophysical Journal (2016). DOI: 10.3847/0004-637X/822/1/42 , On Arxiv: arxiv.org/abs/1602.02779.

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Gold Member
But, the third peak in the CDM is largely a consequence of the hypothesis that dark matter is collisionless, so if the strongest evidence for the DM paradigm is the LambdaCDM paradigm (and on that point I tend to agree with you), then non-collisionless dark matter hypotheses are really serious problem with the model.
Approximately collisionless. The extent to which dark matter interacts with itself and other matter has far less of an impact on the CMB than it does on late-time data sets.

A summary of the small scale problems with LambdaCDM from an author who just a few weeks ago wrote a controversial paper claiming that the alleged universal acceleration scale of MOND doesn't exist (i.e. a modified gravity skeptic) explains this in the follow, understated, abstract:
And? Small scale cosmological data sets are inherently more difficult to model, making it far more challenging to link data and experiment. The large-scale success of the theory (with the CMB being the most dramatic large-scale data set) is an extremely powerful piece of evidence. It argues, very strongly, for the correct way forward to be more likely found in minor modifications to ##\Lambda##CDM (such as with regard to the temperature and interaction cross-section of dark matter) than to a complete overhaul.

If an alternative theory cannot match those large-scale successes, it's not worth considering. MOND has historically had a very, very hard time with that.

Gold Member
And? Small scale cosmological data sets are inherently more difficult to model, making it far more challenging to link data and experiment. The large-scale success of the theory (with the CMB being the most dramatic large-scale data set) is an extremely powerful piece of evidence. It argues, very strongly, for the correct way forward to be more likely found in minor modifications to ##\Lambda##CDM (such as with regard to the temperature and interaction cross-section of dark matter) than to a complete overhaul.

Minor modifications won't do the job. You don't create systemic relationships like the MOND toy model that explains in a predictive manner a very wide range of phenomena in which inferred dark matter distributions are finely related to ordinary matter distributions in an extremely wide range of circumstances, with just a minor tweak. Dark matter particle theories have yet to make any prospective predictions of observations of new kinds of phenomena that have panned out. They don't explain why the data is so well organized in such a simple way. You need a mutually exclusive set of parameters for a dark matter cross-section of interaction to fit the data. This is a huge problem. This is why simply heavy cold dark matter theories have been almost completely abandoned in favor of more complex theories that also add new dark forces.

If an alternative theory cannot match those large-scale successes, it's not worth considering. MOND has historically had a very, very hard time with that.

So far as I can tell, there is just a single data point (prediction of the CBM distribution) that favors DM particles over modified gravity theories, and there is really no data whatsoever that modified gravity theories don't accurately predict the CBM distribution. Sure, MOND itself, a very simple, non-relativistic toy model, isn't going to work in that kind of situation. But, that doesn't mean that relativistic modified gravity theories are disfavored.

Gold Member
Minor modifications won't do the job. You don't create systemic relationships like the MOND toy model that explains in a predictive manner a very wide range of phenomena in which inferred dark matter distributions are finely related to ordinary matter distributions in an extremely wide range of circumstances, with just a minor tweak. Dark matter particle theories have yet to make any prospective predictions of observations of new kinds of phenomena that have panned out. They don't explain why the data is so well organized in such a simple way. You need a mutually exclusive set of parameters for a dark matter cross-section of interaction to fit the data. This is a huge problem. This is why simply heavy cold dark matter theories have been almost completely abandoned in favor of more complex theories that also add new dark forces.
You're really diverging from anything that can be supported by evidence here.

Gold Member
You're really diverging from anything that can be supported by evidence here.

More evidence. Also what other than CMB have dark matter particle theories accurately predicted prospectively in new kinds of phenomena?

Here's a review of the state of dark matter particle research by someone not really known for having any strong advocacy position:

Recent high-resolution simulations that include Cold Dark Matter (CDM) and baryons have shown that baryonic physics can dramatically alter the dark matter structure of galaxies. These results modify our predictions for observed galaxy evolution and structure. Given these updated expectations, it is timely to re-examine observational constraints on the dark matter model. A few observations are reviewed that may indirectly trace dark matter, and may help confirm or deny possible dark matter models. Warm Dark Matter (WDM) and Self-Interacting Dark Matter (SIDM) are currently the favorite alternative models to CDM. Constraints on the WDM particle mass require it to be so heavy that WDM is nearly indistinguishable from CDM. The best observational test of SIDM is likely to be in the dark matter distribution of faint dwarf galaxies, but there is a lack of theoretical predictions for galaxy structure in SIDM that account for the role of baryons.

Alyson Brooks, "Re-Examining Astrophysical Constraints on the Dark Matter Model" (July 28, 2014). A year later, Brooks is co-author of an article that compares CDM to SIDM in simulations with baryonic matter feedback and finds that the differences are surprisingly modest.

The problems with conventional Cold Dark Matter models that were used in the formulation of LambdaCDM, requiring a fifth force or some other major revision to the theory have been well known for many years:

Dark matter (DM) self-interactions have important implications for the formation and evolution of structure, from dwarf galaxies to clusters of galaxies. We study the dynamics of self-interacting DM via a light mediator, focusing on the quantum resonant regime where the scattering cross section has a non-trivial velocity dependence. While there are long-standing indications that observations of small scale structure in the Universe are not in accord with the predictions of collisionless DM, theoretical study and simulations of DM self-interactions have focused on parameter regimes with simple analytic solutions for the scattering cross section, with constant or classical velocity (and no angular) dependence. We devise a method that allows us to explore the velocity and angular dependence of self-scattering more broadly, in the strongly-coupled resonant and classical regimes where many partial modes are necessary for the achieving the result. We map out the entire parameter space of DM self-interactions --- and implications for structure observations --- as a function of the coupling and the DM and mediator masses. We derive a new analytic formula for describing resonant s-wave scattering. Finally, we show that DM self-interactions can be correlated with observations of Sommerfeld enhancements in DM annihilation through indirect detection experiments. . . .

As is well known, the collisionless cold DM (CCDM) paradigm has been highly successful in accounting for large scale structure of the Universe. However, it is far from clear that this paradigm can also successfully explain the small scale structure of the Universe. Precision observations of dwarf galaxies show DM distributions with cores, in contrast to cusps predicted by CCDM simulations. It has also been shown that the most massive subhalos in CCDM simulations of Miky Way (MW) size halos are too dense to host the observed brightest satellites of the MW. Lastly, chemo-dynamic measurements in at least two MW dwarf galaxies show that the slopes of the DM density profiles are shallower than predicted by CCDM simulations. These small scale anomalies, taken at face value, may indicate that other interactions besides gravity play a role in structure formation.

Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure Authors:Sean Tulin, Hai-Bo Yu, Kathryn M. Zurek (Submitted on 15 Feb 2013).

Another examination of conventional cold dark matter models is more vehement. Here are some key quotes from the abstract and body text:

Evidence that Cold Dark Matter (LambdaCDM) and its proposed tailored cures do not work at small scales is staggering. . . .The most troubling signs of the failure of the CDM paradigm have to do with the tight coupling between baryonic matter and the dynamical signatures of DM in galaxies, e.g. the Tully-Fisher relation, the stellar disc-halo conspiracy, the maximum disc phenomenon, the MOdified Newtonian Dynamics (MOND) phenomenon, the baryonic Tully-Fisher relation, the baryonic mass discrepancy-acceleration relation, the 1-parameter dimensionality of galaxies, and the presence of both a DM and a baryonic mean surface density. . . .It should be recalled that the connection between small scale structure features and the mass of the DM particle follows mainly from the value of the free-streaming length lfs. Structures smaller than lfs are erased by free-streaming. WDM particles with mass in the keV scale produce lfs ∼ 100 kpc while 100 GeV CDM particles produce an extremely small lfs ∼ 0.1 pc. While the keV WDM lfs ∼ 100 kpc is in nice agreement with the astronomical observations, the GeV CDM lfs is a million times smaller and produces the existence of too many small scale structures till distances of the size of the Oort’s cloud in the solar system. No structures of such type have ever been observed. Also, the name CDM precisely refers to simulations with heavy DM particles in the GeV scale. . . . The mass of the DM particle with the free-streaming length naturally enters in the initial power spectrum used in the N-body simulations and in the initial velocity. The power spectrum for large scales beyond 100 kpc is identical for WDM and CDM particles, while the WDM spectrum is naturally cut off at scales below 100 kpc, corresponding to the keV particle mass free-streaming length. In contrast, the CDM spectrum smoothly continues for smaller and smaller scales till ∼ 0.1 pc, which gives rise to the overabundance of predicted CDM structures at such scales. . . . Overall, seen in perspective today, the reasons why CDM does not work are simple: the heavy wimps are excessively non-relativistic (too heavy, too cold, too slow), and thus frozen, which preclude them to erase the structures below the kpc scale, while the eV particles (HDM) are excessively relativistic, too light and fast, (its free streaming length is too large), which erase all structures below the Mpc scale; in between, WDM keV particles produce the right answer.

H.J. de Vega and N.G. Sanchez, “Warm dark matter in the galaxies:theoretical and observational progresses. Highlights and conclusions of the chalonge meudon workshop 2011″ (14 Sept 2011) http://arxiv.org/abs/1109.3187 See also in accord S. Tulin, et al. “Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure” (15 Feb 2013) http://arxiv.org/abs/1302.3898:

As is well known, the collisionless cold DM (CCDM) paradigm has been highly successful in accounting for large scale structure of the Universe. . . . Precision observations of dwarf galaxies show DM distributions with cores, in contrast to cusps predicted by CCDM simulations. It has also been shown that the most massive subhalos in CCDM simulations of Miky Way (MW) size halos are too dense to host the observed brightest satellites of the MW. Lastly, chemo-dynamic measurements in at least two MW dwarf galaxies show that the slopes of the DM density profiles are shallower than predicted by CCDM simulations.

Again, the NFW profile predicted for collisionless or almost collisionless dark matter simply does not fit the data.

In cosmological N-body simulations, the baryon effects on the cold dark matter (CDM) halos can be used to solve the small scale problems in ΛCDM cosmology, such as cusp-core problem and missing satellites problem. It turns out that the resultant total density profiles (baryons plus CDM), for halos with mass ranges from dwarf galaxies to galaxy clusters, can match the observations of the rotation curves better than NFW profile. In our previous work, however, we found that such density profiles fail to match the most recent strong gravitational lensing observations. In this paper, we do the converse: we fit the most recent strong lensing observations with the predicted lensing probabilities based on the so-called (α,β,γ) double power-law profile, and use the best-fit parameters (α=3.04,β=1.39,γ=1.88) to calculate the rotation curves. We find that, at outer parts for a typical galaxy, the rotation curve calculated with our fitted density profile is much lower than observations and those based on simulations, including the NFW profile. This again verifies and strengthen the conclusions in our previous works: in ΛCDM paradigm, it is difficult to reconcile the contradictions between the observations for rotation curves and strong gravitational lensing.

Lin Wang, Da-Ming Chen, Ran Li "The total density profile of DM halos fitted from strong lensing" (July 31, 2017). As the body text explains:

It is now well established that, whatever the manners the baryon effects are included in the collisionless CDM N-body cosmological simulations, if the resultant density profiles can match the observations of rotation curves, they cannot simultaneously predict the observations of strong gravitational lensing (under- or over-predict). And for the case of typical galaxies, the reverse is also true, namely, the SIS profile preferred by strong lensing cannot be supported by the observations of rotation curves near the centers of galaxies.

Brooks, above, suggests that Warm Dark Matter theories don't solve the problems of cold dark matter very well even with baryon effects. Warm dark matter models also have their own problems (in accord see here).

It has long been known that small scale structure strongly disfavors a mix of warm and cold dark matter. Warm dark matter models also have great difficulty forming dwarf galaxies that we know exist (also, see, e.g. here, and here).

Recent research constrains warm dark matter models to have masses approximately in the range of 1-2 keV and also tightly bounds their possible self-interactions. The observed Tully-Fisher relation is inconsistent with lighter warm dark matter particles. Observations of the Andromeda Galaxy suggest an upper limit on warm dark matter particle sizes of about 2.2 keV. Long gamma ray burst data imposes similar constraints placing a floor value of about 1.6-1.8 keV for combined limits from the various sources of 1.6-2.2 keV. This is a very narrow window of parameter space in which the a lambdaCDM theory consistent particle could work. See also deVega and Sanchez, "Dark matter in galaxies: the dark matter particle mass is about 2 keV" (Submitted on 2 Apr 2013) http://arxiv.org/abs/1304.0759 See also, for example, C. Watso, et al. “Constraining Sterile Neutrino Warm Dark Matter with Chandra Observations of the Andromeda Galaxy” http://arxiv.org/abs/1111.4217 (10 Jan 2012) (WDM mass capped at 2.2 keV); R. de Souza, A. Mesinger, A. Ferrara, Z. Haiman, R. Perna, N. Yoshida, “Constraints on Warm Dark Matter models from high-redshift long gamma-ray bursts” (17 Apr 2013) http://arxiv.org/abs/1303.5060 (WMD mass at least 1.6 keV); D. Anderhaldena, et al. “Hints on the Nature of Dark Matter from the Properties of Milky Way Satellites” (12 Dec 2012) http://arxiv.org/pdf/1212.2967v1.pdf (mixed CDM/WDM models disfavored); J. Viñas, et al. “Typical density profile for warm dark matter haloes” (9 Jul 2012) http://arxiv.org/abs/1202.2860 (models with more than one WDM species disfavored); Xi Kang, Andrea V. Maccio, aaron A. dutton, "The effect of Warm Dark Matter on galaxy properties: constraints from the stellar mass function and the Tully-Fisher relation" (8 April 2013) http://arxiv.org/abs/1208.0008 (WDM mass of more than 0.75 keV and consistent with 2 keV).

More on the scatter of the Tully-Fischer relation v. LCDM.

In a LCDM cosmology, the baryonic Tully-Fisher relation (BTFR) is expected to show significant intrinsic scatter resulting from the mass-concentration relation of dark matter halos and the baryonic-to-halo mass ratio. We study the BTFR using a sample of 118 disc galaxies (spirals and irregulars) with data of the highest quality: extended HI rotation curves (tracing the outer velocity) and Spitzer photometry at 3.6 μm (tracing the stellar mass). Assuming that the stellar mass-to-light ratio (M*/L) is nearly constant at 3.6 μm, we find that the scatter, slope, and normalization of the BTFR systematically vary with the adopted M*/L. The observed scatter is minimized for M*/L > 0.5, corresponding to nearly maximal discs in high-surface-brightness galaxies and BTFR slopes close to ~4. For any reasonable value of M*/L, the intrinsic scatter is ~0.1 dex, below general LCDM expectations. The residuals show no correlations with galaxy structural parameters (radius or surface brightness), contrary to the predictions from some semi-analytic models of galaxy formation. These are fundamental issues for LCDM cosmology.

Federico Lelli, Stacy S. McGaugh, and James M. Schombert, "The small scatter of the baryonic Tully-Fisher relation" (December 14, 2015).

More generally dark matter distributions closely track baryon distributions even though there is no viable mechanism to do so. See, e.g. Edo van Uitert, et al., "Halo ellipticity of GAMA galaxy groups from KiDS weak lensing" (October 13, 2016).

The more we go deep into the knowledge of the dark component which embeds the stellar component of galaxies, the more we realize the profound interconnection between them. We show that the scaling laws among the structural properties of the dark and luminous matter in galaxies are too complex to derive from two inert components that just share the same gravitational field. In this paper we review the 30 years old paradigm of collisionless dark matter in galaxies. We found that their dynamical properties show strong indications that the dark and luminous components have interacted in a more direct way over a Hubble Time. The proofs for this are the presence of central cored regions with constant DM density in which their size is related with the disk length scales. Moreover we find that the quantity ρDM(r,L,RD)ρ⋆(r,L,RD) shows, in all objects, peculiarities very hardly explained in a collisionless DM scenario.

Paolo Salucci and Nicola Turini, "Evidences for Collisional Dark Matter In Galaxies?" (July 4, 2017).

But, this can't simply be remedied by tweaking the cross-section of interaction between ordinary matter and dark matter because XENON1T an LUX and other direct dark matter detection experiments place tight constraints on the maximum cross-section of interaction that dark matter can have with ordinary matter, which limits the extent to which non-gravitational interactions with baryons can account for the tight correlations of baryonic matter and inferred dark matter distributions.

We report the first dark matter search results from XENON1T, a ∼2000-kg-target-mass dual-phase (liquid-gas) xenon time projection chamber in operation at the Laboratori Nazionali del Gran Sasso in Italy and the first ton-scale detector of this kind. The blinded search used 34.2 live days of data acquired between November 2016 and January 2017. Inside the (1042±12) kg fiducial mass and in the [5, 40] keVnr energy range of interest for WIMP dark matter searches, the electronic recoil background was (1.93±0.25)×10−4 events/(kg × day ×keVee), the lowest ever achieved in a dark matter detector. A profile likelihood analysis shows that the data is consistent with the background-only hypothesis. We derive the most stringent exclusion limits on the spin-independent WIMP-nucleon interaction cross section for WIMP masses above 10 GeV/c2, with a minimum of 7.7 ×10−47 cm2 for 35-GeV/c2 WIMPs at 90% confidence level.

From here. The XENON1T exclusion range is slightly more strict than LUX. Xenon 1T has replicated this exclusion and hence made more robust to all manner of systemic errors. The LHC also provides data that exclude potential dark matter cross-sections of interactions, particularly at lower masses which direct dark matter detection experiments struggle to probe. See e.g. https://arxiv.org/abs/1709.02304 and https://arxiv.org/abs/1510.01516

As Jester at Resonaances explains (a professional physicist and blogger):

One possible scenario is that WIMPs experience one of the Standard Model forces, such as the weak or the Higgs force. The former option is strongly constrained by now. If WIMPs had interacted in the same way as our neutrino does, that is by exchanging a Z boson, it would have been found in the Homestake experiment. Xenon1T is probing models where the dark matter coupling to the Z boson is suppressed by a factor cχ ~ 10^-3 - 10^-4 compared to that of an active neutrino.

Incidentally, the close bounds emerging at the LHC on deviations from the Standard Model predictions for Higgs boson decays and branching fractions, also increasingly forecloses the possibility of "Higgs portal" dark matter over a wide range of its parameter space, a loophole that might have escaped direct dark matter detection experiments like LUX and XENON1T.

Collisionless bosonic dark matter is likewise excluded over a wide range of parameters.

We know that self-interactions between dark matter particles with each other with cross-sections of interaction on the order of 10^-23 to 10^-24 greatly improve the fit to the halo models observed (self-interactions on the order of 10^-22 or more, or of 10^25 or more, clearly do not produce the observed halos). Notably, this cross section of self-interaction is fairly similar to the cross-section of interaction of ordinary matter (e.g. helium atoms) with each other. So, if dark matter halos are explained by self-interaction, the strength of that self-interaction ought to be on the same order of magnitude as electromagnetic interactions.

But, our observations and simulations are now sufficiently precise that we can determine that ultimately, a simple constant coupling constant between dark matter particles or velocity dependent coupling constant between dark matter particles fails to fit the observed dark matter halos. Generically, these models generate shallow spherically symmetric halos which are inconsistent with the comparatively dense and ellipsoidal halos that are observed.

Next generation self-interacting dark matter models look at more a general Yukawa potential generated by dark matter to dark matter forces with massive force carriers (often called "dark photons") that have masses which empirically need to be on the order of 1 MeV to 100 MeV (i.e. between the mass of an electron and a muon, but less than the lightest hadron, the pion, which has a mass on the order of 135-140 MeV) to produce dark halos that are a better fit to the dark matter halos that are observed. But, the XENON experiment places strong limits on interactions between ordinary photons and "dark photons".

Axion Dark Matter

Axion dark matter models are a poor fit to the CMB data that is among the strongest reasons to support a dark matter hypothesis. Renée Hlozek, David J. E. Marsh, Daniel Grin "Using the Full Power of the Cosmic Microwave Background to Probe Axion Dark Matter" (August 18, 2017).

Galaxy Cluster Bounds For Dark Matter

Galaxy clusters that MOND struggles with are also problematic for a wide range of dark matter particle theories, and suggest hot dark matter neutrino solutions for the discrepancies there, contrary to LambdaCDM models.

Galaxy clusters, employed by Zwicky to demonstrate the existence of dark matter, pose new stringent tests. If merging clusters demonstrate that dark matter is self-interacting with cross section σ/m∼2 cm2/gr, MACHOs, primordial black holes and light axions that build MACHOs are ruled out as cluster dark matter.

Recent strong lensing and X-ray gas data of the quite relaxed and quite spherical cluster A1835 allow to test the cases of dark matter with Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distribution, next to Navarro-Frenck-White profiles. Fits to all these profiles are formally rejected at over 5σ, except in the fermionic situation.The interpretation in terms of (nearly) Dirac neutrinos with mass of 1.61+0.19−0.30 eV/c2 is consistent with results on the cluster A1689, with the WMAP, Planck and DES dark matter fractions and with the nondetection of neutrinoless double β-decay. The case will be tested in the 2018 KATRIN experiment.

Theodorus Maria Nieuwenhuizen "Subjecting dark matter candidates to the cluster test" (October 3, 2017).

A variety of searches for sterile neutrinos have also ruled out this possibility in the relevant mass range. See, e.g., https://arxiv.org/abs/1710.06488 and http://iopscience.iop.org/article/10.1088/1742-6596/718/3/032008/pdf

More Astronomy Evidence Problems with Mass Assembly In LambdaCDM

The speed of the El Gordo galaxy collision (2200 km/second) is a problem for LambdaCDM. See Sandor M. Molnar, Tom Broadhurst. A HYDRODYNAMICAL SOLUTION FOR THE “TWIN-TAILED” COLLIDING GALAXY CLUSTER “EL GORDO”. The Astrophysical Journal, 2015; 800 (1): 37 DOI: 10.1088/0004-637X/800/1/37 which notes:

The distinctive cometary X-ray morphology of the recently discovered massive galaxy cluster "El Gordo" (ACT-CT J0102–4915; z = 0.87) indicates that an unusually high-speed collision is ongoing between two massive galaxy clusters. A bright X-ray "bullet" leads a "twin-tailed" wake, with the Sunyaev-Zel'dovich (SZ) centroid at the end of the northern tail. We show how the physical properties of this system can be determined using our FLASH-based, N-body/hydrodynamic model, constrained by detailed X-ray, SZ, and Hubble lensing and dynamical data. The X-ray morphology and the location of the two dark matter components and the SZ peak are accurately described by a simple binary collision viewed about 480 million years after the first core passage. We derive an impact parameter of
300 kpc, and a relative initial infall velocity of
2250 km s–1 when separated by the sum of the two virial radii assuming an initial total mass of 2.15 × 1015 M ☉ and a mass ratio of 1.9.
Our model demonstrates that tidally stretched gas accounts for the northern X-ray tail along the collision axis between the mass peaks, and that the southern tail lies off axis, comprising compressed and shock heated gas generated as the less massive component plunges through the main cluster. The challenge for ΛCDM will be to find out if this physically extreme event can be plausibly accommodated when combined with the similarly massive, high-infall-velocity case of the Bullet cluster and other such cases being uncovered in new SZ based surveys.

As noted earlier in the thread, this is not the only galaxy collision whose details are a poor fit for ΛCDM. One fluke is a fluke. Multiple galaxy collisions with velocities well out of line with ΛCDM predictions is more than a fluke, it is a problem with the theory.

ΛCDM would like to look to galaxy evolution details which are obscure and varied to explain its shortcomings, but they don't, instead, the need to rely on galaxy evolution is a problem because reasonably galaxy evolution hypotheses don't fit the data:

We show that a significant correlation (up to 5sigma) emerges between the bulge index, defined to be larger for larger bulge/disk ratio, in spiral galaxies with similar luminosities in the Galaxy Zoo 2 of SDSS and the number of tidal-dwarf galaxies in the catalogue by Kaviraj et al. (2012). In the standard cold or warm dark-matter cosmological models the number of satellite galaxies correlates with the circular velocity of the dark matter host halo. In generalized-gravity models without cold or warm dark matter such a correlation does not exist, because host galaxies cannot capture in-falling dwarf galaxies due to the absence of dark-matter-induced dynamical friction. However, in such models a correlation is expected to exist between the bulge mass and the number of satellite galaxies, because bulges and tidal-dwarf satellite galaxies form in encounters between host galaxies. This is not predicted by dark matter models in which bulge mass and the number of satellites are a priori uncorrelated because higher bulge/disk ratios do not imply higher dark/luminous ratios. Hence, our correlation reproduces the prediction of scenarios without dark matter, whereas an explanation is not found readily from the a priori predictions of the standard scenario with dark matter. Further research is needed to explore whether some application of the standard theory may explain this correlation.

Martin Lopez-Corredoira and Pavel Kroupa, "The number of tidal dwarf satellite galaxies in dependence of bulge index" (November 30, 2015).

Occam's Razor

Of course, one of the reasons to favor a dark matter particle approach in the first place was Occam's Razor. Adding one new particle to the mix (when many beyond the Standard Model theories predict that such particles exist and that at least some are stable) would be less of an extension of current theory than a tweak to general relativity. But, when you get into the current system where you start needing not just new particles, but new fundamental forces of Nature and Byzantine constraints on matter assembly in the universe with no obvious physical basis, this becomes much more problematic.

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Gold Member
You still haven't addressed my fundamental concern, a concern which is noted in at least some of your sources: galaxy formation and structure are not well-understood period. We just do not have a good enough modeling of galaxy behavior to make strong statements about what dark matter models say or don't say on small scales.

If your objections to a theory rely solely upon the subset of observations where the link between data and theory is most tenuous, then your objections might as well be baseless.

Gold Member
You still haven't addressed my fundamental concern, a concern which is noted in at least some of your sources: galaxy formation and structure are not well-understood period. We just do not have a good enough modeling of galaxy behavior to make strong statements about what dark matter models say or don't say on small scales.

If your objections to a theory rely solely upon the subset of observations where the link between data and theory is most tenuous, then your objections might as well be baseless.

Small Scale Structure Is Well Understood And Actually Rather Simple

We understand galaxy structure much better than you claim. And, sixty-one citations to academic journal articles by professional physicists in this thread support the claim that this kind of data is not "baseless". There are no academic journal articles out there that support your claim that:

We just do not have a good enough modeling of galaxy behavior to make strong statements about what dark matter models say or don't say on small scales.

Even strong supports of dark matter particle theories don't make that claim, as articles that I have cited and quoted from demonstrate. An N-body problem with a very high N full of objects governed by general relativity in a weak field regime where general relativity is indistinguishable from Newtonian gravity is simply not as complicated as you claim when it comes to explaining the current behavior and dynamics of galaxy scale systems which have quite non-eccentric distributions of luminous matter, and in which dark matter distributions, by hypothesis based upon the properties that define them, simply cannot be to terribly complicated or structured either.

There is lots and lots of data, the data shows robust and consistent patterns over a huge range of phenomena that can be summed up very simply, and the data isn't that hard to analyze.

Galaxy formation is less well understood, but it is also a part of what any successful cosmology model including LambdaCDM must address and does address. But, in many circumstances where LambdaCDM does address this, it is demonstrably inaccurate.

Moreover, while a modified gravity theory can be complete without a galaxy formation theory, a dark matter particle theory without an explanation for how dark matter gets distributed in the universe so as to have the effects that are observed is not even wrong. It isn't a theory. It is a non-testable hunch or a paradigm from which to generate theories.

You are taking the position that dark matter particle theories can't predict anything on small scales. That isn't exactly a proposition that inspires confidence and it isn't enough to establish that this is the correct or consensus conclusion. It can't be right because it isn't even an answer.

But, this position is not the one taken by investigators who are actually working on dark matter particle theories. Scott Dodelson, for example, is much more ambivalent (please read the comments by Benoit Famaey (a professional academic physicist in the field) and Stacy McGaugh (a leading proponent of MOND-like theories) as well) (see also this paper in PNAS which likewise isn't nearly so dismissive of modified gravity approaches). As Faemey explains:

The crucial point is that these novel properties should lead to a unique relation between the distribution of ‘normal’ matter (baryons) and the gravitational field in galaxies. Such a one-to-one relation is in contradiction with the a priori expectations from the standard cosmological model, because the different histories and environments of individual galaxies should a priori not lead to such a unique relation between the dark matter and baryon distributions. On the other hand, such a one-to-one matching is at the core of the MOND paradigm, which actually defines such a universal relation (Milgrom’s relation) between the distribution of baryons and the gravitational field in galaxies. This relation is indeed observed, and has not been falsified in galaxies for the last 30 years: since this is an empirical fact, calling it ‘bad science’ or pseudoscience can only be a misinformed statement.

Indeed, in my view, the observational success of Milgrom’s relation in galaxies is very interesting because the history of physics has taught us that the devil was often hidden in such ‘details’. In the present case, the detail will for sure either:

1) Teach us something fundamental about the galaxy formation process (this is the ‘CDM must reduce to MONDian phenomenology’ argument), or

2) Teach us something fundamental about the very nature of the dark sector, or

3) Teach us something new and fundamental about gravity and dynamics.

Either way, what makes it really cool is that it makes a lot of succesful predictions that cannot be made from LambdaCDM: just as examples, it predicted the shape of rotation curves of Low Surface Brightness galaxies before these objects had even been detected, and more recently predictions on the internal velocity dispersions of two satellite galaxies of Andromeda by McGaugh and Milgrom were subsequently confirmed by Tollerud et al. (http://arxiv.org/abs/1302.0848). On the other hand, a lot of also really cool theoretical properties can be studied (e.g. http://arxiv.org/abs/1202.1723), which allows us to slice and combine observational data in different ways than in the standard picture.

Now, IMO, this MOND relation cannot, by itself, really be called a theory: MOND is a paradigm based on a general (and observationally successful) relation to which different actual MOND-theories (TeVeS, BIMOND, dipolar dark fluid, entropic gravity, etc.) must conform. As they all boil down to the same metric as General Relativity in the static weak-field limit, but with a boosted weak-field potential, gravitational lensing by galaxies is not a problem (http://arxiv.org/abs/0804.2668). As also pointed by Scott Dodelson, these theories mostly modify the fundamental Lagrangian of nature by adding new terms and new degrees of freedom, which can be thought of as parts of the ‘dark sector’ of the Universe, akin to dark energy fields: this makes Options 2 and 3 hereabove somewhat entangled with each other. . . . it is grossly exaggerated for people on twitter or anywhere to state that there has been no recent progress at all concerning addressing large-scale structure or CMB-related issues in MOND-theories. All these theories might fail in the end, but given the observed phenomenology on small scales, they are definitely worth investigating, and if anyone has a new idea based on entropic gravity (http://arxiv.org/abs/1106.4108) or any other framework (see http://arxiv.org/abs/1106.4984), to explain the MOND relation, such new theories are worth developing and investigating too. It is however very clear that, at the end of the road, such a theory would necessarily have to naturally reproduce the successes of LambdaCDM on large scales. This is not easy and it is absolutely fair to say that there is currently no alternative which does as well on large scales as LambdaCDM. Note however that, given currently existing theories, this could perhaps be due to lack of manpower.

McGaugh notes in another comment at the same post:

It is true that the simplest ansatz for a MOND prediction of the CMB acoustic power spectrum was consistent with the original Boomerang data. It is also true that the data improved over time. The part relevant to MOND – the first-to-second peak amplitude ratio – was not wrong (d’oh!). Indeed, part of the no-CDM prediction was that the second peak would appear out of the noise at a very particular value. That is exactly what happened. The 1:2 peak amplitude ratio observed by WMAP is EXACTLY as predicted by McGaugh (1999 http://adsabs.harvard.edu/abs/1999ApJ…523L..99M). Where the simple no-CDM ansatz that gets the 1:2 ratio right fails is in the 2:3 peak height ratio. I have never said otherwise. No one can honestly imply that I have ignored these issues, or myself been dishonest about them. Indeed, I take the issue of the third peak very seriously, and have commented on it (long ago!) on my own website (http://astroweb.case.edu/ssm/mond/).

A full article by Famaey and McGaugh on the topic can be found here.

In another discussion between physicists, including Sean Carroll (who has also authored article in the field) as the main advocate for particle dark matter, McGaugh make the following observation:

You imply that it is hanging on to vain hope to explain the third peak of the CMB by anything other than a new source. I am saying that it is a vain hope to imagine that turning the crank on any number of CDM numerical simulations is ever going to spit out the observed MONDian phenomenology. Just because LCDM works for the CMB does not automatically guarantee that it’ll work in galaxies, any more than MOND’s success in galaxies means it must inevitably succeed as a the basis of a cosmological theory.

There is a very simple empirical result in the data for galaxies that cosmologists have, by and large, simply ignored. The stated excuse is usually something like “well, galaxies are complicated, non-linear structures” and so we should be excused from explaining them. Indeed, in LCDM galaxies probably should be complicated. But they’re not. They’re simple. So simple, the obey a single effective force law. Fitting that with dark matter is like fitting epicylces to planetary orbits. Of course you can do it – you have an infinite number of free parameters. But it don’t make no sense.

I have said for years now that they conclusion you come to depends on how you weigh the evidence. The CMB is an important piece of that evidence. So are rotation curves. It is not obvious to me that the third peak should count 100% and galaxies zero. Yet that is in effect the weighting that lots of people appear to be using.

Dark Matter Is Not A Unique Solution To Fitting The CMB Data

There is also no evidence that almost collisionless dark matter is the only way that the CMB results can be produced. It is a very simple theory that produces the right answer (through an exceedingly complex analysis of lots of very complex and messy data (see also here) that has been artfully tamed in an incredible but sophisticated and complex accomplishment).

It is also worth recalling that while the existence of a third-peak is a prediction of LambdaCDM, the height of the third-peak that is observed is not. The height of the third-peak that is observed in LambdaCDM is one of the primary means by which an experimentally measured parameter of the LambdaCDM theory, the ratio of dark matter to ordinary matter in the universe, is measured in a model dependent way. This makes the accomplishment of LambdaCDM in predicting dark matter rather less impressive.

MOND itself, of course, isn't relativistic so shouldn't by itself do anything more than provide some guidance for how to generalize it. But, MOND is not the only modified gravity theory out there. (A survey at some of the more theoretically driven, as opposed to phenomenologically driven modified gravity theories can be found here).

Indeed, qualitatively relativistic modifications of gravity along MOND lines do predict a third-peak (this theory is called TeVeS and is discussed Bekenstein who devised it in this 2011 article) just as dark matter does, although the precise prediction hasn't been calculated with sufficient precision to compare it to the actual CMB data. Even if that particular modified gravity extension of MOND gets it wrong (spoiler alert: TeVeS was ultimately found to get it wrong), it is proof of principle that dark matter particles are not the exclusive means by which to reproduce the CMB results.

The very large scale structure prediction of MOND-like theories is that structure formation precedes more rapidly than in LambdaCDM, and this seems to be born out by the evidence so far as noted in a previous comment on this threat.

It is possible in principle to fit any of several classes of modified gravity theories to match the CMB data as well. Literature documenting another successful fit is referenced in this powerpoint presentation (Nagata-TC=Sugiyama, 2004) which I haven't searched for myself yet. More recently, an analysis of the Planck 2015 results by the Planck Collaboration confirmed that it is possible to fit a class of modified gravity fields that change the gravitational force with respect to all matter baryonic or otherwise, to produce results compatible with those observed (see page 27) if parameters are set appropriately, as well as with a variety of other gravity modification (most of which pertain to dark energy phenomena). In particular, Moffat's MOG modified gravity theory, which has also accurately described the Bullet Cluster example and galactic cluster data, matches the CMB data.

Differences between some modified gravity models and LambdaCDM can, in principle, even be distinguished from the Planck data itself, if the Planck data are integrated with certain other astronomy data sets related to the distributions of observed galaxies.