We propose a novel theory of dark matter (DM) superfluidity that matches the successes of the ΛCDM 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 ∼ ρ 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. Identifying a precise cold atom analogue would give important insights on the microphysical interactions underlying DM superfluidity. Tantalizingly, it might open the possibility of simulating the properties and dynamics of galaxies in laboratory experiments.

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.

In massive gravity the so-far-found black hole solutions on Minkowski space happen to convert horizons into a certain type of singularities. Here we explore whether these singularities can be avoided if space-time is not asymptotically Minkowskian. We find an exact analytic black hole (BH) solution which evades the above problem by a transition at large scales to self-induced de Sitter (dS) space-time, with the curvature scale set by the graviton mass. This solution is similar to the ones discovered by Koyama, Niz and Tasinato, and by Nieuwenhuizen, but differs in detail. The solution demonstrates that in massive GR, in the Schwarzschild coordinate system, a BH metric has to be accompanied by the Stückelberg fields with nontrivial backgrounds to prevent the horizons to convert into the singularities. We also find an analogous solution for a Reissner-Nordström BH on dS space. A limitation of our approach, is that we find the solutions only for specific values of the two free parameters of the theory, for which both the vector and scalar fluctuations loose their kinetic terms, however, we hope our solutions represent a broader class with better behaved perturbations.

We study Galileon theories that emerge in ghost-free massive gravity. In particular, we focus on a sub-class of these theories where the Galileons can be completely decoupled from the tensor Lagrangian. These Galileons differ from generic ones -- they have interrelated coefficients of the cubic and quartic terms, and most importantly, a non-standard coupling to external stress-tensors, governed by the same coefficient. We show that this theory has no static stable spherically symmetric solutions that would interpolate from the Vainshtein region to flat space; these two regions cannot be smoothly matched for the sign of the coefficient for which fluctuations are stable. Instead, for this sign choice, a solution in the Vainshtein domain is matched onto a cosmological background. Small fluctuations above this solution are stable, and sub-luminal. We discuss observational constraints on this theory, within the quantum effective Lagrangian approach, and argue that having a graviton mass of the order of the present-day Hubble parameter, is consistent with the data. Last but not least, we also present a general class of cosmological solutions in this theory, some of which exhibit the de-mixing phenomenon, previously found for the self-accelerated solution.Comment: 17 pages; Typos correcte

We propose a unified framework that reconciles the stunning success of MOND on galactic scales with the triumph of the ΛCDM model on cosmological scales. This is achieved through the physics of superfluidity. Dark matter consists of self-interacting axion-like particles that thermalize and condense to form a superfluid in galaxies, with ∼mK critical temperature. The superfluid phonons mediate a MOND acceleration on baryonic matter. Our framework naturally distinguishes between galaxies (where MOND is successful) and galaxy clusters (where MOND is not): dark matter has a higher temperature in clusters, and hence is in a mixture of superfluid and normal phase. The rich and well-studied physics of superfluidity leads to a number of striking observational signatures.The standard Λ Cold Dark Matter (ΛCDM) model does very well at fitting large scale observables. On galactic scales, however, a number of challenges have emerged. Disc galaxies display a tight correlation between total baryonic mass and asymptotic velocity, M b ∼ v 4 c , known as the Baryonic Tully-Fisher Relation (BTFR) [1,2]. Hydrodynamical simulations can reproduce the BTFR by tuning baryonic feedback processes, but their stochastic nature naturally results in a much larger scatter [3]. Furthermore, the mass [4,5] and phase-space [6-9] distributions of dwarf satellites in the Local Group are puzzling.A radical alternative is MOdified Newtonian Dynamics (MOND) [10], which replaces dark matter (DM) with a modification of gravity at low acceleration: a a N (a N a 0 ); a √ a N a 0 (a N a 0 ), with best-fit value a 0 1.2 × 10 −8 cm/s 2 . This empirical force law has been remarkably successful at explaining a wide range of galactic phenomena [11]. In the MOND regime, a test particle orbits an isolated source according to v 2 /r = G N M b a 0 /r 2 . This gives a constant asymptotic velocity, v 2 c = √ G N M b a 0 , which in turn implies the BTFR. The empirical success of MOND, however, is limited to galaxies. The predicted temperature profile in galaxy clusters conflicts with observations [12]. The Tensor-Vector-Scalar (TeVeS) relativistic extension [13] fails to reproduce the CMB and matter spectra [14,15]. The lensing features of merging clusters [16,17] are problematic [18]. This has motivated various hybrid proposals that include both DM and MOND, e.g., [19][20][21][22][23].In this Letter, together with a longer companion paper [24], we propose a novel framework that unifies the DM and MOND phenomena through the physics of superfluidity. Our central idea is that DM forms a superfluid inside galaxies, with a coherence length of order the size of galaxies. The critical temperature is ∼ mK, which intriguingly is comparable to Bose-Einstein condensation (BEC) critical temperatures for cold atom gases. Indeed, in many ways our DM behaves like cold dark atoms.The superfluid nature of DM dramatically changes its macroscopic behavior in galaxies. Instead of evolving as independent particles, DM is more aptly described as collective excitations. Superfluid phonons,...