Milgrom's Law Research Articles

Dark Matter Superfluidity

In these lectures I describe a theory of dark matter superfluidity developed in the last few years. The dark matter particles are axion-like, with masses of order eV. They Bose-Einstein condense into a superfluid phase in the central regions of galaxy halos. The superfluid phonon excitations in turn couple to baryons and mediate a long-range force (beyond Newtonian gravity). For a suitable choice of the superfluid equation of state, this force reproduces the various galactic scaling relations embodied in Milgrom's law. Thus the dark matter and modified gravity phenomena represent different phases of a single underlying substance, unified through the rich and well-studied physics of superfluidity.

Phenomenological consequences of superfluid dark matter with baryon-phonon coupling

Recently, a new form of dark matter has been suggested to naturally reproduce the empirically successful aspects of Milgrom's law in galaxies. The dark matter particle candidates are axion-like, with masses of order eV and strong self-interactions. They Bose-Einstein condense into a superfluid phase in the central regions of galaxy halos. The superfluid phonon excitations in turn couple to baryons and mediate an additional long-range force. For a suitable choice of the superfluid equation of state, this force can mimic Milgrom's law. In this paper we develop in detail some of the main phenomenological consequences of such a formalism, by revisiting the expected dark matter halo profile in the presence of an extended baryon distribution. In particular, we show how rotation curves of both high and low surface brightness galaxies can be reproduced, with a slightly rising rotation curve at large radii in massive high surface brightness galaxies, thus subtly different from Milgrom's law. We finally point out other expected differences with Milgrom's law, in particular in dwarf spheroidal satellite galaxies, tidal dwarf galaxies, and globular clusters, whose Milgromian or Newtonian behavior depends on the position with respect to the superfluid core of the host galaxy. We also expect ultra-diffuse galaxies within galaxy clusters to have velocities slightly above the baryonic Tully-Fisher relation. Finally, we note that, in this framework, photons and gravitons follow the same geodesics, and that galaxy-galaxy lensing, probing larger distances within galaxy halos than rotation curves, should follow predictions closer to the standard cosmological model than those of Milgrom's law.

Modified Newtonian Dynamics (MOND) as a Modification of Newtonian Inertia

We present a modified inertia formulation of Modified Newtonian dynamics (MOND) without retaining Galilean invariance. Assuming that the existence of a universal upper bound, predicted by MOND, to the acceleration produced by a dark halo is equivalent to a violation of the hypothesis of locality (which states that an accelerated observer is pointwise inertial), we demonstrate that Milgrom's law is invariant under a new space-time coordinate transformation. In light of the new coordinate symmetry, we address the deficiency of MOND in resolving the mass discrepancy problem in clusters of galaxies.

MILGROM’S LAW AND Λ’S SHADOW: HOW MASSIVE GRAVITY CONNECTS GALACTIC AND COSMIC DYNAMICS

Massive gravity provides a natural solution for the dark energy problem of cosmology and is also a candidate for resolving the dark matter problem. I demonstrate that, assuming reasonable scaling relations, massive gravity can provide for Milgrom's law of gravity (or "modified Newtonian dynamics") which is known to remove the need for particle dark matter from galactic dynamics. Milgrom's law comes with a characteristic acceleration, Milgrom's constant, which is observationally constrained to $a_0\approx1.1\times10^{-10}$ m/s$^2$. In the derivation presented here, this constant arises naturally from the cosmologically required mass of gravitons like $a_0\propto c\sqrt{\Lambda}\propto c H_0\sqrt{3\Omega_{\Lambda}}$, with $\Lambda$, $H_0$, and $\Omega_{\Lambda}$ being the cosmological constant, the Hubble constant, and the third cosmological parameter, respectively. My derivation suggests that massive gravity could be the mechanism behind both, dark matter and dark energy.

Local Group timing in Milgromian dynamics

The Local Group timing has been one of the first historical probes of the missing mass problem. Whilst modern cosmological probes indicate that pure baryonic dynamics is not sufficient on the largest scales, nearby galaxies and small galaxy groups persistently obey Milgrom's MOND law, which implies that dynamics at small scales is possibly entirely predicted by the baryons. Here, we investigate the Local Group timing in this context of Milgromian dynamics. Making use of the latest measured proper motions and radial velocities for Andromeda and the Magellanic clouds, we integrate backwards their orbits by making use of the Milgromian two-body equation of motion. We find that, with the currently measured proper motions and radial velocity of M31, MOND would imply that the Milky Way and M31 first moved apart via Hubble expansion after birth, but then necessarily got attracted again by the Milgromian gravitational attraction, and had a past fly-by encounter before coming to their present positions. This encounter would most probably have happened 7 to 11 Gyr ago (0.8<z<3). The absence of a dark matter halo and its associated dynamical friction is necessary for such a close encounter not to trigger a merger. Observational arguments which could exclude or favour such a past encounter would thus be very important in view of falsifying or vindicating Milgromian dynamics on the scale of the Local Group. Interestingly, the closest approach of the encounter is small enough (<55 kpc) to have severe consequences on the disk dynamics, including perhaps thick disk formation, and on the satellite systems of both galaxies. The ages of the satellite galaxies and of the young halo globular clusters, all of which form the vast polar structure around the Milky Way, are consistent with these objects having been born in this encounter.

A WDM model for the evolution of galactic halos

It is a well-known fact that the gravitational effect of dark matter in galaxies is only noticeable when the orbitalaccelerations drop below a0 ≃ 2 × 10−8 cm s−1 (Milgrom's Law). This peculiarity of the dynamic behaviour of galaxies was initially ascribed to a modificationof Newtonian dynamics (MOND theory) and, consequently, it was used as an argument to criticize the dark matter hypothesis. In our model, warm dark matter is composedby collisionless Vlasov particles with a primordial typical velocity≃ 330 km s−1 and, consequently, they evaporatedfrom galactic cores and reorganized in halos with a cusp at a finite distance from the galactic center (in contrast with Cold Dark Mattersimulations which predict a cusp at the center of galaxies). This is confirmed by mean-field N-body simulationsof the self-gravitating Vlasov dark matter particles in the potential well of the baryonic core. The rest mass of these particles, μ, is determined from a kinetic theory of the early universe with a cosmological constant. We find thatμ is in the range of a few keV. This result makes sterile neutrinos the best suited candidates forthe main component of dark matter.

Reconciling MOND and dark matter?

Observations of galaxies suggest a one-to-one analytic relation between the inferred gravity of dark matter at any radius and the enclosed baryonic mass, a relation summarized by Milgrom's law of modified Newtonian dynamics (MOND). However, present-day covariant versions of MOND usually require some additional fields contributing to the geometry, as well as an additional hot dark matter component to explain cluster dynamics and cosmology. Here, we envisage a slightly more mundane explanation, suggesting that dark matter does exist but is the source of MOND-like phenomenology in galaxies. We assume a canonical action for dark matter, but also add an interaction term between baryonic matter, gravity, and dark matter, such that standard matter effectively obeys the MOND field equation in galaxies. We show that even the simplest realization of the framework leads to a model which reproduces some phenomenological predictions of cold dark matter (CDM) and MOND at those scales where these are most successful. We also devise a more general form of the interaction term, introducing the medium density as a new order parameter. This allows for new physical effects which should be amenable to observational tests in the near future. Hence, this very general framework, which can be furthermore related to a generalized scalar-tensor theory, opens the way to a possible unification of the successes of CDM and MOND at different scales.

How Cold Dark Matter Theory Explains Milgrom’s Law

Milgrom noticed the remarkable fact that the gravitational effect of dark matter in galaxies only becomes important where accelerations are less than about 10-8 cm s-2 ~ cH0 (Milgrom's law). This forms the basis for modified Newtonian dynamics, an alternative to particle dark matter. However, any successful theory of galactic dynamics must account for Milgrom's law. We show how Milgrom's law comes about in the cold dark matter theory of structure formation.