The cold dark-matter model successfully explains both the emergence and evolution of cosmic structures on large scales and, when we include a cosmological constant, the properties of the homogeneous and isotropic Universe. However, the cold dark-matter model faces persistent challenges on the scales of galaxies. Indeed, N-body simulations predict some galaxy properties that are at odds with the observations. These discrepancies are primarily related to the dark-matter distribution in the innermost regions of the halos of galaxies and to the dynamical properties of dwarf galaxies. They may have three different origins: (1) the baryonic physics affecting galaxy formation is still poorly understood and it is thus not properly included in the model; (2) the actual properties of dark matter differs from those of the conventional cold dark matter; (3) the theory of gravity departs from General Relativity. Solving these discrepancies is a rapidly evolving research field. We illustrate some of the solutions proposed within the cold dark-matter model, and solutions when including warm dark matter, self-interacting dark matter, axion-like particles, or fuzzy dark matter. We also illustrate some modifications of the theory of gravity: Modified Newtonian Dynamics (MOND), MOdified Gravity (MOG), and $f\left(R\right)$ gravity.

We develop a formalism to help calculate in quantum field theory the departures from the description of a system by classical field equations. We apply the formalism to a homogeneous condensate with attractive contact interactions and to a homogeneous self-gravitating condensate in critical expansion. In their classical descriptions, such condensates persist forever. We show that in their quantum description, parametric resonance causes quanta to jump in pairs out of the condensate into all modes with wave vector less than some critical value. We calculate, in each case, the time scale over which the homogeneous condensate is depleted and after which a classical description is invalid. We argue that the duration of classicality of inhomogeneous condensates is shorter than that of homogeneous condensates.

Axions and axionlike particles are bosonic quantum fields. They are often assumed to follow classical field equations due to their high degeneracy in the phase space. In this work, we explore the disparity between classical and quantum field treatments in the context of density and velocity fields of axions. Once the initial density and velocity fields are specified, the evolution of the axion fluid is unique in the classical field treatment. However, in the quantum field treatment, there are many quantum states consistent with the given initial density and velocity field. We show that evolutions of the density perturbations for these quantum states are not necessarily identical and, in general, differ from the unique classical evolution. To illustrate the underlying physics, we consider a system of large number of bosons in a one-dimensional box, moving under the gravitational potential of a heavy static point mass. We ignore the self-interactions between the bosons here. Starting with homogeneous number density and zero velocity field, we determine the density perturbations in the linear regime in both quantum and classical field theories. We find that classical and quantum evolutions are identical in the linear regime if only one single-particle state is occupied by all the bosons and the self-interaction is absent. If more than one single-particle states are occupied, the density perturbations in quantum evolutions differ from the classical prediction after a certain time which depends upon the parameters of the system.

We propose a new method for determining the shape of the gravitational potential of the dark matter (DM) halo of the Milky Way (MW) with the galactocentric tangential velocities of a sample of hypervelocity stars (HVSs). We compute the trajectories of different samples of HVSs in a MW where the baryon distribution is axisymmetric and the DM potential either is spherical or is spheroidal or triaxial with radial-dependent axis ratios. We create ideal observed samples of HVSs with known latitudinal components of the tangential velocity,v_ϑ, and azimuthal component of the tangential velocity,v_φ. We determine the shape of the DM potential with the distribution of |v_ϑ| when the Galactic potential is axisymmetric, or with the distribution of |v_ϑ| and of a function, $ \bar{v}_{\varphi} $, ofv_φwhen the Galactic potential is non-axisymmetric. We recover the correct shape of the DM potential by comparing the distribution of |v_ϑ| and $ \bar{v}_{\varphi} $ of the ideal observed sample against the corresponding distributions of mock samples of HVSs that traveled in DM halos of different shapes. We use ideal observed samples of ∼800 HVSs, which are the largest samples of 4M_⊙HVSs ejected with the Hills mechanism at a rate ∼10⁻⁴yr⁻¹, currently outgoing, and located at more than 10 kpc from the Galactic Center. In our ideal case of galactocentric velocities with null uncertainties and no observational limitations, the method recovers the correct shape of the DM potential with a success rateS ≳ 89% when the Galactic potential is axisymmetric, andS > 96% in the explored non-axisymmetric cases. The unsuccessful cases yield axis ratios of the DM potential that are off by ±0.1. The success rate decreases with decreasing size of the HVS sample: for example, for a spherical DM halo,Sdrops from ∼98% to ∼38% when the sample size decreases from ∼800 to ∼40 HVSs. Accurate estimates of the success rate of our method applied to real data require more realistic samples of mock observed HVSs. Nevertheless, our analysis suggests that a robust determination of the shape of the DM potential requires the measure of the galactocentric velocity of a few hundred HVSs of robustly confirmed galactocentric origin.

We show that measuring the velocity components of hypervelocity stars (HVSs) can discriminate between modified Newtonian dynamics (MOND) and Newtonian gravity. Hypervelocity stars are ejected from the Galactic center on radial trajectories with a null tangential velocity component in the reference frame of the Galaxy. They acquire tangential components due to the nonspherical components of the Galactic gravitational potential. Axisymmetric potentials only affect the latitudinal components, v_θ, and non-null azimuthal components, v_ϕ, originate from non-axisymmetric matter distributions. For HVSs with sufficiently high ejection speed, the azimuthal velocity components are proportionate to the deviation of the gravitational potential from axial symmetry. The ejection velocity threshold is ∼750 km s⁻¹ for 4 M_⊙ stars and increases with decreasing HVS mass. We determine the upper limit of v_ϕ as a function of the galactocentric distance for these high-speed HVSs if MOND, in its quasi-linear formulation QUMOND, is the correct theory of gravity and either the triaxial Galactic bulge or a nonspherical hot gaseous halo is the primary source of the azimuthal component, v_ϕ. In Newtonian gravity, the HVSs within 60 kpc of the Galactic center may easily have v_ϕ values higher than the QUMOND upper limit if the dark matter halo is triaxial or if the dark matter halo and the baryonic components are axisymmetric but their two axes of symmetry are misaligned. Therefore, even a limited sample of high-speed HVSs could in principle allow us to distinguish between the QUMOND scenario and the dark matter model. This test is currently limited by (i) the lack of a proper procedure to assess whether a star originates from the Galactic center and thus is indeed an HVS in the model one wishes to constrain; and (ii) the large uncertainties on the galactocentric azimuthal velocity components, which should be reduced by at least a factor of ∼10 to make this test conclusive. A proper procedure to assess the HVS nature of the observed stars and astrometric measurements with microarcsecond precision would make this test feasible.