# MOND theory primer

Gold Member
The astronomer Stacy McGaugh has become the most prominent public promoter of MOND (modified Newtonian dynamics) in recent years, on the grounds that it makes many successful predictions, yet according to the standard "LambdaCDM" (dark energy plus cold dark matter) paradigm, there's no reason it should be getting anything right. In his latest paper he says this again, and provides a list of references for a theoretical research program that would build on these successes:

https://www.sciencedirect.com/science/article/pii/S0039368121000728
Testing galaxy formation and dark matter with low surface brightness galaxies
Stacy S. McGaugh
MOND is an incomplete depiction of reality, lacking as yet a satisfactory relativistic extension that incorporates the known successes of General Relativity. The logical inference is that MOND may be pointing the way towards a deeper theory of dynamics that incorporates both (Milgrom, 2020). The obvious research program would seek to build on these successes (Bekenstein, 2004; Berezhiani & Khoury, 2015; Blanchet, 2007; Famaey et al., 2018; Merritt, 2017; Milgrom, 2006, 2009; Skordis et al., 2006; Skordis and Zlosnik, 2020; Skordis and Złośnik, 2019). By extension, research programs that fail to incorporate these successes are doomed to fail. Examples include experimental searches for non-baryonic dark matter (e.g, WIMPs) and theories devised without this input (e.g., warm dark matter, self-interacting dark matter, and so on).

Here are the eleven papers he mentions:

https://arxiv.org/abs/1910.04368
MOND vs. dark matter in light of historical parallels
Mordehai Milgrom
MOND is a paradigm that contends to account for the mass discrepancies in the Universe without invoking dark' components, such as dark matter' and dark energy'. It does so by supplanting Newtonian dynamics and General Relativity, departing from them at very low accelerations. Having in mind readers who are historians and philosophers of science, as well as physicists and astronomers, I describe in this review the main aspects of MOND -- its statement, its basic tenets, its main predictions, and the tests of these predictions -- contrasting it with the dark-matter paradigm. I then discuss possible wider ramifications of MOND, for example the potential significance of the MOND constant, a0, with possible implications for the roots of MOND in cosmology.
Along the way I point to parallels with several historical instances of nascent paradigms. In particular, with the emergence of the Copernican world picture, that of quantum physics, and that of relativity, as regards their initial advent, their development, their schematic structure, and their ramifications. For example, the interplay between theories and their corollary laws, and the centrality of a new constant with converging values as deduced from seemingly unrelated manifestations of these laws. I demonstrate how MOND has already unearthed a number of unsuspected laws of galactic dynamics (to which, indeed, a0 is central) predicting them a priori, and leading to their subsequent verification. I parallel the struggle of the new with the old paradigms, and the appearance of hybrid paradigms at such times of struggle. I also try to identify in the history of those established paradigms a stage that can be likened to that of MOND today.

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.70.083509
Relativistic gravitation theory for the modified Newtonian dynamics paradigm
Jacob D. Bekenstein
The modified Newtonian dynamics (MOND) paradigm of Milgrom can boast of a number of successful predictions regarding galactic dynamics; these are made without the assumption that dark matter plays a significant role. MOND requires gravitation to depart from Newtonian theory in the extragalactic regime where dynamical accelerations are small. So far relativistic gravitation theories proposed to underpin MOND have either clashed with the post-Newtonian tests of general relativity, or failed to provide significant gravitational lensing, or violated hallowed principles by exhibiting superluminal scalar waves or an a priori vector field. We develop a relativistic MOND inspired theory which resolves these problems. In it gravitation is mediated by metric, a scalar, and a 4-vector field, all three dynamical. For a simple choice of its free function, the theory has a Newtonian limit for nonrelativistic dynamics with significant acceleration, but a MOND limit when accelerations are small.
We calculate the β and γ parameterized post-Newtonian coefficients showing them to agree with solar system measurements. The gravitational light deflection by nonrelativistic systems is governed by the same potential responsible for dynamics of particles. To the extent that MOND successfully describes dynamics of a system, the new theory’s predictions for lensing by that system’s visible matter will agree as well with observations as general relativity’s predictions made with a dynamically successful dark halo model. Cosmological models based on the theory are quite similar to those based on general relativity; they predict slow evolution of the scalar field. For a range of initial conditions, this last result makes it easy to rule out superluminal propagation of metric, scalar, and vector waves.

https://arxiv.org/abs/1507.01019
Theory of Dark Matter Superfluidity
Lasha Berezhiani, Justin Khoury
We propose a novel theory of dark matter (DM) superfluidity that matches the successes of the LambdaCDM model on cosmological scales while simultaneously reproducing the MOdified Newtonian Dynamics (MOND) phenomenology on galactic scales. The DM and MOND components have a common origin, representing different phases of a single underlying substance. DM consists of axion-like particles with mass of order eV and strong self-interactions. The condensate has a polytropic equation of state P~rho^3 giving rise to a superfluid core within galaxies. Instead of behaving as individual collisionless particles, the DM superfluid is more aptly described as collective excitations. Superfluid phonons, in particular, are assumed to be governed by a MOND-like effective action and mediate a MONDian acceleration between baryonic matter particles.
Our framework naturally distinguishes between galaxies (where MOND is successful) and galaxy clusters (where MOND is not): due to the higher velocity dispersion in clusters, and correspondingly higher temperature, the DM in clusters is either in a mixture of superfluid and normal phase, or fully in the normal phase. The rich and well-studied physics of superfluidity leads to a number of observational signatures: array of low-density vortices in galaxies, merger dynamics that depend on the infall velocity vs phonon sound speed; distinct mass peaks in bullet-like cluster mergers, corresponding to superfluid and normal components; interference patters in super-critical mergers. Remarkably, the superfluid phonon effective theory is strikingly similar to that of the unitary Fermi gas, which has attracted much excitement in the cold atom community in recent years. The critical temperature for DM superfluidity is of order mK, comparable to known cold atom Bose-Einstein condensates.

https://arxiv.org/abs/astro-ph/0605637
Gravitational polarization and the phenomenology of MOND
Luc Blanchet
The modified Newtonian dynamics (MOND) has been proposed as an alternative to the dark matter paradigm; the philosophy behind is that there is no dark matter and we witness a violation of the Newtonian law of dynamics. In this article, we interpret differently the phenomenology sustaining MOND, as resulting from an effect of "gravitational polarization", of some cosmic fluid made of dipole moments, aligned in the gravitational field, and representing a new form of dark matter. We invoke an internal force, of non-gravitational origin, in order to hold together the microscopic constituents of the dipole. The dipolar particles are weakly influenced by the distribution of ordinary matter; they are accelerated not by the gravitational field, but by its gradient, or tidal gravitational field.

https://arxiv.org/abs/1712.01316
Emergence of the mass discrepancy-acceleration relation from dark matter-baryon interactions
Benoit Famaey, Justin Khoury, Riccardo Penco
The observed tightness of the mass discrepancy-acceleration relation (MDAR) poses a fine-tuning challenge to current models of galaxy formation. We propose that this relation could arise from collisional interactions between baryons and dark matter (DM) particles, without the need for modification of gravity or ad hoc feedback processes. We assume that these interactions satisfy the following three conditions: (i) the relaxation time of DM particles is comparable to the dynamical time in disk galaxies; (ii) DM exchanges energy with baryons due to elastic collisions; (iii) the product between the baryon-DM cross section and the typical energy exchanged in a collision is inversely proportional to the DM number density. We present an example of a particle physics model that gives a DM-baryon cross section with the desired density and velocity dependence.
Direct detection constraints require our DM particles to be either very light (m<<mb) or very heavy (m>>mb), corresponding respectively to heating and cooling of DM by baryons. In both cases, our mechanism applies and an equilibrium configuration can in principle be reached. Here, we focus on the heavy DM/cooling case as it is technically simpler. Under these assumptions, we find that rotationally-supported disk galaxies could naturally settle to equilibrium configurations satisfying a MDAR at all radii without invoking finely tuned feedback processes. We also discuss issues related to the small scale clumpiness of baryons, as well as predictions for pressure-supported systems. We argue in particular that galaxy clusters do not follow the MDAR despite being DM-dominated because they have not reached their equilibrium configuration. Finally, we revisit existing phenomenological, astrophysical and cosmological constraints on baryon-DM interactions in light of the unusual density dependence of the cross section.

https://arxiv.org/abs/1703.02389
Cosmology and Convention
David Merritt
I argue that some important elements of the current cosmological model are "conventionalist" in the sense defined by Karl Popper. These elements include dark matter and dark energy; both are auxiliary hypotheses that were invoked in response to observations that falsified the standard model as it existed at the time. The use of conventionalist stratagems in response to unexpected observations implies that the field of cosmology is in a state of "degenerating problemshift" in the language of Imre Lakatos. I show that the "concordance" argument, often put forward by cosmologists in support of the current paradigm, is weaker than the convergence arguments that were made in the past in support of the atomic theory of matter or the quantization of energy.

https://arxiv.org/abs/astro-ph/0510117
MOND as Modified Inertia
Mordehai Milgrom
I briefly highlight the salient properties of modified-inertia formulations of MOND, contrasting them with those of modified-gravity formulations, which describe practically all theories propounded to date. Future data (e.g. the establishment of the Pioneer anomaly as a new physics phenomenon) may prefer one of these broad classes of theories over the other. I also outline some possible starting ideas for modified inertia.

https://arxiv.org/abs/0912.0790
Bimetric MOND gravity
Mordehai Milgrom
A new relativistic formulation of MOND is advanced, involving two metrics as independent degrees of freedom: the MOND metric g_mn, to which alone matter couples, and an auxiliary metric g*_mn. The main idea hinges on the fact that we can form tensors from the difference, C^a_bc, of the Levi-Civita connections of the two metrics, and these act like gravitational accelerations. In the context of MOND we can form dimensionless acceleration' scalars, and functions thereof, from contractions of C^a_bc/a0. I look at a class of bimetric MOND theories governed by an action with the gravitational Lagrangian density b sqrt(g)R+a sqrt(g*) R* -2(gg*)^{1/4}f(k)a0^2M(U/a0^2), and with matter actions I(g_mn,psi)+I*(g*_mn,chi), with U a scalar quadratic in the C^a_bc, k=(g/g*)^{1/4}, and allowing for the existence of twin matter, chi, that couples to g*_mn alone. In particular, I concentrate on one interesting and simple choice of the scalar U.
This theory introduces only one new constant, a0; it tends simply to General Relativity in the limit a0 goes to 0, and to a phenomenologically valid MOND theory in the nonrelativistic limit. The theory naturally gives MOND and "dark energy" effects from the same term in the action, both controlled by the MOND constant a0. As regards gravitational lensing by nonrelativistic systems--a holy grail for relativistic MOND theories--the theory predicts that the same potential that controls massive-particle motion also dictates lensing in the same way as in GR. This last result can be modified with other choices of U, but lensing is still enhanced and MOND-like, with an effective logarithmic potential.

https://arxiv.org/abs/astro-ph/0505519
Large Scale Structure in Bekenstein's theory of relativistic Modified Newtonian Dynamics
C. Skordis, D. F. Mota, P. G. Ferreira, C. Boehm
A relativistic theory of modified gravity has been recently proposed by Bekenstein. The tensor field in Einstein's theory of gravity is replaced by a scalar, a vector, and a tensor field which interact in such a way to give Modified Newtonian Dynamics (MOND) in the weak-field non-relativistic limit. We study the evolution of the universe in such a theory, identifying its key properties and comparing it with the standard cosmology obtained in Einstein gravity. The evolution of the scalar field is akin to that of tracker quintessence fields. We expand the theory to linear order to find the evolution of perturbations on large scales. The impact on galaxy distributions and the cosmic microwave background is calculated in detail. We show that it may be possible to reproduce observations of the cosmic microwave background and galaxy distributions with Bekenstein's theory of MOND.

https://arxiv.org/abs/2007.00082
A new relativistic theory for Modified Newtonian Dynamics
Constantinos Skordis, Tom Zlosnik
We propose a relativistic gravitational theory leading to Modified Newtonian Dynamics, a paradigm that explains the observed universal acceleration and associated phenomenology in galaxies. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed Cosmic Microwave Background and matter power spectra on linear cosmological scales. We show that its action expanded to 2nd order is free of ghost instabilities and discuss its possible embedding in a more fundamental theory.

https://arxiv.org/abs/1905.09465
A general class of gravitational theories as alternatives to dark matter where the speed of gravity always equals the speed of light
Constantinos Skordis, Tom Zlosnik
A number of theories of gravity have been proposed as proxies for dark matter in the regime of galaxies and cosmology. The recent observations of gravitational waves (GW170817) from the merger of two neutron stars, followed by an electromagnetic counterpart (GW170817a) have placed stringent constraints on the difference of the speed of gravity to the speed of light, severely restricting the phenomenological viability of such theories. We revisit the impact of these observations on the Tensor-Vector-Scalar (TeVeS) paradigm of relativistic Modified Newtonian Dynamics (MOND) and demonstrate the existence of a previously unknown class of this paradigm where the speed of gravity always equals the speed of light. We show that this holds without altering the usual (bimetric) MOND phenomenology in galaxies.

ohwilleke and Demystifier

I know many physicists are at odds with [MOND/MOG] because of the incredible success of General Relativity so far.
That's not why they're generally "at odds with MOND/MOG". Read Stacy McGaugh's blog for some fascinating (but also depressing) insights into the sociology of all this.

Note that Sabine Hossenfelder has her own MOG theory (involving a preferred vector field that also acts like a superfluid), which seems to line up with some aspects of galactic rotation curve phenomenology. Afaict, it does not propose any fundamental origin for that vector field, much like Verlinde's nonrelativistic MOG theory which inspired Sabine's, afaict.

jedishrfu
Note that Sabine Hossenfelder has her own MOG theory (involving a preferred vector field that also acts like a superfluid), which seems to line up with some aspects of galactic rotation curve phenomenology. Afaict, it does not propose any fundamental origin for that vector field, much like Verlinde's nonrelativistic MOG theory which inspired Sabine's, afaict.
I still don't understand why this is called modified gravity! It seems like unmodified gravity plus matter. If you consider say the elctromagnetic field and its stress energy tensor, that goes in the Einstein's equations, you don't call that modified gravity. How is this vector field any different?

I still don't understand why this is called modified gravity! It seems like unmodified gravity plus matter. If you consider say the electromagnetic field and its stress energy tensor, that goes in the Einstein's equations, you don't call that modified gravity. How is this vector field any different?
Have you studied Verlinde's original paper? (If you haven't, then good luck! It's excruciatingly opaque.) He tries to obtain a distinguished vector field by considering entropy associated with horizons, hence the vector field can be considered as intrinsic to the geometry. That's what makes the term "modified" gravity reasonable.

Unfortunately, Verlinde's paper was shown to have a crucial error at one point -- I don't recall the authors now, but following the cited-by links should find it. Afaik, Verlinde didn't respond to that criticism.

In Sabine's case, she explicitly doesn't embrace Verlinde's idea that the distinguished field is an analogue of the displacement vector field in standard elasticity theory. She also postulates some unusual superfluid-like properties for the vector field. I think it's just a type of "Einstein-Aether" theory (terrible name -- it means Einstein GR with a distinguished vector field), but Sabine told me emphatically that hers is different because of certain details of the properties of the vector field, and the unusual couplings in her Lagrangian.

I remain skeptical.

I meant Sabine's. If I remember correctly she adds a term to the Lagrangian, but doesn't change the gemetric part of the Lagrangian. So why is this modified gravity?! It looks like normal gravity plus additianal matter.

Gold Member
What is your take on MOND?

I know many physicists are at odds with it because of the incredible success of General Relativity so far.

What is MOND?

MOND, in the strict sense, is a toy model phenomenological theory with a limited domain of applicability. It applies only in the regime where General Relativity is customarily approximated for all practical purposes by Newtonian gravity, i.e. where the gravitational fields of General Relativity are predicted to be extremely weak and the objects in question are moving at speed much less than the speed of light.

How weak?

The gravitational field of the Sun alone falls to that strength at a distance of about 1,052 billion km (about 7000 astronomical units (AU). This is about 1/9th of the light year from the Sun, which is about 175 times the average distance of Pluto from the Sun.

The "Newtonian" regime of MOND, above a specified gravitational field strength, is understood by all MOND advocates to be General Relativity in the regime where the predictions of General Relativity in strong fields is distinguishable from Newtonian gravity. Likewise, even though Newtonian gravity in the strict sense doesn't bend light, a gravitational field of a given strength in MOND is assumed to have the same effect on massless particles with mass-energy, such as photons, as it does in General Relativity.

In the MOND regime of MOND, the strength of a weak gravitational field is predicted to be greater than it would be if Newtonian gravity applied, by a simply formula which is consistent with the observed flat rotation curve speeds of objects at the fringes of galaxies.

MOND does not obey the "Einstein equivalence principle" that: "The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime."

Instead, it predicts an "external field effect" which reduces the enhancement of Newtonian gravity arising in the MOND regime in weak gravitational fields when the objects that are gravitationally attracted to each other are within the gravitational fields of other objects that bring the total gravitational field acting on an object close to or above the threshold gravitational field strength at which the MOND regime begins. There is significant (model dependent) observational evidence to support the existence of the external field effect that MOND predicts.

MOND doesn't have any deep underlying theoretical basis or mechanism.

MOND is notable, despite this limited range of applicability, because it is very simple, has only of physical constant in excess of Newtonian gravity, and was one of the first modified gravity theories proposed to explain dark matter phenomena without dark matter. Applying MOND without dark matter is a good approximation of what is observed in all circumstances except strong gravitational fields/relativistic speed objects where General Relativity is materially different from Newtonian gravity, up to the largest isolated galaxies. It has repeatedly been used to correctly predict new, unobserved phenomena.

MOND has known defects. It underestimates the magnitude of dark matter phenomena in galactic cluster scale systems by roughly an order of magnitude. It also can't be applied to cosmology questions without being at least partially generalized relativistically, and there is no single clear way to do so.

Why does MOND matter?

Developing Intuition About The Physical Impact Of DM Phenomena

This said, the more important thing to understand about MOND is that it is basically a heuristic rule of thumb for understanding what dark matter phenomena are doing physically.

Proof of Concept That Modified Gravity Theories Can Work

It is also a proof of concept that dark matter phenomena can be explained over a very wide domain of applicability with even a very crude gravity modification. The fact that it is possible to closely approximate the main phenomenological implications of dark matter theories over an extremely broad range of applicability with a crude and simple tweak to the law of gravity with no theoretical basis, suggests that it might be possible to reproduce all dark matter phenomena with a more sophisticated gravitational tweak, one which might also have a better developed theoretical basis that leads to accurate predicts in the cases where MOND in the strict sense is imperfect.

Tight Constraints On DM Theories That They Have To Explain

The observational validity of MOND, to close to the limits of observational data, also poses a serious challenge to any competing dark matter particle theory. Specifically:

1. The physical effects of dark matter particle theories need to be possible to predict, with a high degree of precision, solely from the detailed distribution of the ordinary matter in a galaxy scale or smaller system, and must track the idiosyncrasies of the system's matter distribution.

2. Identical distributions of ordinary matter should have identical inferred dark matter distributions.

3. The physical effects of dark matter particle theories need to be unobservable in gravitational fields from ordinary matter stronger than MOND's physical constant.

4. Systems that would otherwise be expected to exhibit dark matter phenomena in their dynamics should not do so when located in strong enough gravitational fields of nearby distributions of matter.

Nothing in dark matter particle theories obviously suggest that any of these things should be the case. Any dark matter particle theory that doesn't meet these standards (something that can often be discerned analytically from the theory itself), is demonstrably contrary to observational evidence because MOND works in so many cases.

Beyond MOND

MOND proponents are not arguing that MOND, in the strict sense, is a law of nature. They are instead arguing that the successes of MOND provide strong circumstantial evidence that some more sophisticated modification of gravity with a better theoretical justification works.

Once you know what MOND predicts, where it has been validated observationally, and the manner and circumstances in which MOND is contradicted by observational evidence, it is relatively straightforward to develop different, less crude, modifications of gravity that reproduce all of MOND's successes and deals better with the circumstances in which it is flawed.

Among the more sophisticated variants of MOND that utilize its basic insights are John Moffat's MOG theories (see, e.g. Moffat (2020)), some relativistic or partially relativistic generalizations of MOND (see, e.g. Bekenstein (2004) and Skordis (2020)), Verlinde's entropic gravity theory (see, e.g. Verlinde (2016)), toy model theories proposed by physics bloggers Sabine and Lubos respectively, advocates of Conformal Gravity theories (see Nesbet (2014)), and various proponents of scalar-tensor (see, e.g. Sa (2020)), f(R) gravity models (see, e.g. Kuhfittig (2021)) and still other approaches (see, e.g. Sabat (2021), Ghosh (2021) and Gallagher (2021)). There is at least one researcher, Mike McCulloch, actively working on the modified inertia approach to MOND (see e.g. McCulloch (2019)). Work by Alexandre Deur (see, e.g., Deur (2020)) purports to derive MOND-like effects by changing how gravitational field self-interaction effects are operationalized within the context of conventional General Relativity and plain vanilla quantum gravity theories.

These more sophisticated gravity modifications have been successful at tasks such as explaining dark matter phenomena in galactic clusters, explaining the Bullet Cluster, reproducing the cosmic microwave background radiation signatures heralded as evidence of the LambdaCDM paradigm, explaining dark energy without an extra field or substance, providing a more elegant theoretical basis for gravity modification, explaining the impossible early galaxy problem, explaining the 21cm wavelength telescope observations which are contrary to LambdaCDM, and predicting the dynamics of objects in galaxies outside the main galactic plane of the Milky Way.

No one of these theories has met all of these tests simultaneously and most of these theories haven't received a lot of attention for scholars in the larger discipline (or even each other).

This is mostly due to lack of resources directed to this avenue of scholarship. Many of these theories simply haven't received rigorous vetting from scientists other than the proponents of these theories to confirm that the people who have proposed them aren't missing something important. No one has done the work to test anyone of these theories against all the observational evidence, which would require lots of theoretical work to figure out what these theories predict (especially in cosmology settings) and lots of work to digest observational evidence in a manner that can be compared meaningfully to these theoretical predictions.

Early CDM Candidates And Very Massive DM Candidates Are All But Ruled Out

But, it is also true that dark matter particle theories, especially the "Standard Model of Cosmology" as the LambdaCDM theory is known, are much less predictive, and much less of a good fit to the data, than most of its proponents acknowledge.

The idea which was widely accepted when LambdaCDM theory was proposed, that dark matter consists of the lightest supersymmetric particle that is very weakly interacting (probably interacting only via the Standard Model weak force and gravity, just like neutrinos) that were thermal relics from shortly after the Big Bang with a mass on the order of 10-1000 GeV/c^2 has been all but completely ruled out by observational evidence.

Direct dark matter detection experiments have ruled out the existence of particles that interact with ordinary matter as strongly as neutrinos (which also interact only via the weak force and gravity) do in a mass range from about 1 GeV to more than 1000 GeV (dark matter with interactions with ordinary matter identical to neutrinos, which have the same magnitude of weak force charge as all particles in the Standard Model that interact via the weak force) would be detected at the "Z portal cx=1" line in the chart below:

As the chart above shows, even dark matter particles that have interactions with ordinary matters one thousand times weaker than neutrinos (a.k.a. millicharged dark matter) are ruled out for dark matter particle masses of about 10 GeV to 1100 GeV are ruled out experimentally.

The lack of direct detections has been reinforced by the lack of any evidence of beyond the Standard Model particles in high energy physics experiments over a range from MeV to TeV mass candidates (see e.g., the Particle Data Group's experimental exclusions of supersymmetric particles in various mass ranges). Searches for evidence for dark matter from potential signatures of annihilations and decays of dark matter particle candidates have likewise come up empty, despite multiple brief false positive results.

More massive dark matter candidates such as primordial black holes and "MACHOs" (massive compact halo objects) have likewise been all but ruled out by direct detection efforts and other methodologies, although a small mass window for primordial black holes remains simply because no observational technologies are able to rule them out yet.

The shape of dark matter halos inferred from weak lensing data and gravitational dynamics in galaxies and clusters is inconsistent with a particle that has no significant interactions with other dark matter particles or with ordinary matter (something that can be calculated analytically since this kind of dark matter particle is so simple).

There are multiple (i.e more than twenty) significant inconsistencies between cold dark matter theory predictions at both the galaxy and smaller scale, and in cosmological scale observations such as the problem with the 21cm observations shown in the chart below:

(Source).

Some of the other notable problems with lambdaCMD include:

* The gravitational lensing of subhalos in galactic clusters recently observed to be much more compact and less "puffy" than LambdaCDM would predict.

* A KIDS telescope observation of very large scale structure which shows it to be 8.3% smoother (i.e. less clumpy) than predicted by LambdaCDM.

* The Hubble tension (see, e.g., here) that shows that Hubble's constant, which is a measure of the expansion rate of the universe, is about 10% smaller when measured via cosmic microwave background radiation (with a small margin of error) than when measured by a wide variety of measures at times much more removed from the Big Bang that the time at which the cosmic microwave background came into being.

* The halo shapes are usually wrong (too cuspy and not in the NFW distribution predicted by the theory).

* The correspondence between the distribution of ordinary matter and inferred dark matter in galaxies is too tight; truly collisionless dark matter should have less of a tight fit in its distribution to ordinary matter distributions than is observed. This is also the case in galaxy clusters.

* It doesn't explain systemic variation in the amount of apparent dark matter in elliptical galaxies, or why spiral galaxies have smaller proportions of ordinary matter than elliptical galaxies in same sized inferred dark matter halos, or why thick spiral galaxies have more inferred dark matter than thin ones.

* It doesn't explain why satellite galaxies are consistently located in a two dimensional plane relative to the core galaxy.

* Not as many satellite galaxies are observed as predicted, or why the number of satellite galaxies is related to budge mass in spiral galaxies.

* The aggregate statistical distribution of galaxy types and shapes, called the "halo mass function" is wrong.

* Galaxies are observed sooner after the Big Bang than expected (see also here).

* It doesn't explain strong statistical evidence of an external field effect that violates the strong equivalence principle.

* Observations are inconsistent with the "Cosmological principle" that LambdaCDM predicts, which is "the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale.

* It doesn't do a good job of explaining the rare dwarf galaxies (that are usually dark matter dominated) that seem to have no dark matter.

* It doesn't explain deficits of X-ray emissions in low surface brightness galaxies.

* It predicts too few galaxy clusters.

* It doesn't explain evidence of stronger than expected gravitational effects in wide binary stars (also here).

* There are too many galaxy clusters colliding at speeds that are too high relative to each other.

* It doesn't explain the "cosmic coincidence" problem (that the amount of ordinary matter, dark matter and dark energy are of the same order of magnitude at this moment in the history of the Universe since the Big Bang).

* Some of Milky Way's satellites are too dense, requiring the formation masses and redshifts of halos in CDM not compatible with being a satellite.

DM Particle Alternatives To CDMs

So, theoretical efforts to describe dark matter particles have shifted to proposals other than supersymmetric WIMPs.

WDM and ALPs

One approach has been to focus on much less massive particles, primarily "warm dark matter" (WDM) with masses on the order of a keV, and axion-like particles (ALP) with masses ten or more orders of magnitude less massive than neutrinos, both of which can help solve some of the observational problems with CDM with their quantum mechanical properties that make these particle more "wave-like" than WIMP dark matter candidates.

These dark matter candidates can't be "thermal relics" because otherwise they would be "hot dark matter" (i.e. dark matter particles with high mean velocity) which was ruled out early on, but other mechanism to give rise to dark matter candidates can be devised.

These efforts haven't been terribly successful either.

WDM theories have most (although not all) of the problems of CDM theories.

Direct detection and indirect measures have ruled out much of the ALP parameter space, although there is considerable ALP parameter space that isn't rule out by these means.

SIDM and DM with Fifth Forces Candidates

Another approach has been to consider self-interacting dark matter (SIDM) candidates which can resolve problems in the inferred halo shapes, but still fails to address other shortcomings of the CDM paradigm.

Some proposals suggest some sort of very weak interaction with at least some kinds of ordinary matter (although direct dark matter detection experiments strongly constrain these theories as noted above), while others suggest that SIDM can be made to align with ordinary matter distributions as tightly as inferred dark matter halos do with ill-specified or justified feedback mechanisms.

So Far No DM Theories Work

Simply put, no dark matter theory has ever made many significant ex ante predictions of new, unobserved phenomena (other than the cosmic background radiation signature). No dark matter theory describes all of the observational evidence. No dark matter theory has a fully articulated theory to explain why dark matter particles are distributed in such a way that galaxy scale and smaller effects of it are well explained, with only relatively minor deviations, by MOND.

Purported successes of dark matter theories in simulations are mostly the result of highly tuned models, with no clear theoretical basis for their assumptions and lots of fitting parameters (the first one to make a decent fit, a few years ago, had sixteen free parameters to adjust v. one pre-fixed parameter for MOND).

Conclusion: We're Muddling Through

The bottom line is that no single modified gravity or dark matter particle theory works in all circumstances. Moreover, many of the fact patterns where modified gravity theories (or at least MOND) fails are also fact patterns where dark matter theories don't work either.

MOND and progress in related modified gravity theories suggest that modified gravity explanations are viable. But due to a lack of resources devoted to these proposals, are mostly not well vetted. This is disappointing but has an easy solution - more scholarly work on these theories, that is slowly starting to be realized.

DM particle theories have received lots of attention. Most of the simpler one are either ruled out or a strongly disfavored. The most viable ones present not just new particles but also new forces, tipping the balance of Occam's Razor away from these theories and towards modified gravity proposals.

Some scientists are also starting to look a combined modified gravity/DM particle theories to address the shortcomings found in each of these approaches.

Fortunately, unlike high energy physics which is dominated by a handful of big experiments and suffers from a fair amount of "groupthink" in the HEP scientific community, there are myriad important new sources of high quality astronomy and experimental data that are producing a fire hose of new data to consider, and the scientific community is not monolithic in supporting the largely failed LambdaCDM paradigm (which can explain a lot of cosmology measurements with just a few parameters but has both cosmology scale flaws and myriad galaxy and galaxy cluster scale flaws).

The astrophysics community isn't as even handed in its response to modified gravity proposals as I'd like, but real progress is being made, slowly and with one step backward for every two steps forward, but we're getting there and increasingly have the observational data needed to rigorously test all viable modified gravity and DM particle proposals.

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Gold Member
I meant Sabine's. If I remember correctly she adds a term to the Lagrangian, but doesn't change the gemetric part of the Lagrangian. So why is this modified gravity?! It looks like normal gravity plus additianal matter.
Interesting! Can you give a link to her paper, so that I can check by myself?

ohwilleke
Gold Member

Make sure you have at least a pinch of salt, and a bucket, nearby.
[Submitted on 23 Mar 2018]

### The Redshift-Dependence of Radial Acceleration: Modified Gravity versus Particle Dark Matter​

Sabine Hossenfelder, Tobias Mistele
Modified Newtonian Dynamics has one free parameter and requires an interpolation function to recover the normal Newtonian limit. We here show that this interpolation function is unnecessary in a recently proposed covariant completion of Erik Verlinde's emergent gravity, and that Verlinde's approach moreover fixes the function's one free parameter. The so-derived correlation between the observed acceleration (inferred from rotation curves) and the gravitational acceleration due to merely the baryonic matter fits well with data. We then argue that the redshift-dependence of galactic rotation curves could offer a way to tell apart different versions of modified gravity from particle dark matter.
The money chart of this paper (which shows a flaw in particle dark matter theories that it is not observed by astronomers) is this one (citing B. W. Keller, J. W. Wadsley, ApJL 835 L17 (2017) arXiv:1610.06183 [astro-ph.GA]).

This flaw is not shared by MOND or Verlinde's approach that closely match the bold black line in the chart, which represents what astronomers actually observe, at all redshifts. The faint black line in the chart is what would be expected from purely Newtonian gravity without dark matter (which is also what the not rigorously established conventional wisdom of almost all astrophysicists holds is also what the weak field of general relativity without dark matter should look like in galaxies). But see Navia (2018) (arguing for a different modified gravity theory, that the radial acceleration relation actually does not hold at high redshifts).

Obviously, if the simulation of B. W. Keller and J. W. Wadsley relied upon to make that chart accurately portrays what a conventional particle dark matter hypothesis implies, and that isn't what is observed at high redshifts, then the particle dark matter model that they are modeling is not a correct description of reality.

Note also that Keller and Wadsley were arguing their paper from SPARC data that LambdaCDM is consistent with the radial acceleration relation (a cause neutral formulation of the phenomenology implied by MOND), even though as Sabine notes in her paper, this consistency actually only holds at very low redshifts, and falls apart at higher redshifts.

A 2021 paper with essentially the same premise of Keller and Wadsley can be found at https://arxiv.org/abs/2102.13116

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Gold Member
What is your take on MOND?
That in formulating or judging a theory, one should bear in mind the main lines of evidence for dark matter and how dark matter accounts for them, and also the specific successes of MOND and how MOND accounts for those.

The first step is because dark matter does more than account for galactic rotation curves, it also explains anomalous lensing around cluster collisions like the Bullet Cluster; and it's also used to explain the distribution of cosmic background radiation and galactic clusters (via its behavior in the early universe).

The second step is McGaugh's point - there should be a reason why MOND works on galactic scales.

So one could look for a dark matter theory that for some reason behaves like MOND at the galactic scale, e.g. Khoury's superfluid dark matter; or one could look for a modified gravity that also explains other effects attributed to dark matter, e.g. RelMOND is said to also fit the cosmic microwave background. Or you could try both at once; or even none of the above, if you can think of something really new.

Perhaps the most important fact about MOND is that it predicts some phenomenological laws, that do not arise in a generic dark matter theory. One should wish to explain these laws, along with the observations for which dark matter is the usual explanation; and it won't hurt to know how those laws are explained by MOND-based theories.

ohwilleke
Gold Member
The second step is McGaugh's point - there should be a reason why MOND works on galactic scales.
This was my focus immediately upon encountering MOND and for a long time afterwards. It is all good and well to note that it doesn't work perfectly at cluster or greater scales, and that it doesn't have a clear theoretical basis, but if it works as well as it does at galactic scales with a single universal constant and a very simple formula, then any alternative has to provide an explanation for why that happens (and that explanation should probably be pretty simple too).

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