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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.