Self-Similar Growth of Bose Stars.

We analytically solve the problem of Bose star growth in the bath of gravitationally interacting particles. We find that after nucleation of this object, the bath is described by a self-similar solution of the kinetic equation. Together with the conservation laws, this fixes mass evolution of the Bose star. Our theory explains, in particular, the slowdown of the star growth at a certain "core-halo" mass, but also predicts formation of heavier and lighter objects in magistral dark matter models. The developed "adiabatic" approach to self-similarity may be of interest for kinetic theory in general.

Gravitational Bose-Einstein Condensation in the Kinetic Regime.

We study Bose-Einstein condensation and the formation of Bose stars in virialized dark matter halos and miniclusters by universal gravitational interactions. We prove that this phenomenon does occur and it is described by a kinetic equation. We give an expression for the condensation time. Our results suggest that Bose stars may form kinetically in mainstream dark matter models such as invisible QCD axions and fuzzy dark matter.

Relativistic Axions from Collapsing Bose Stars.

The substructures of light bosonic (axionlike) dark matter may condense into compact Bose stars. We study the collapse of critical-mass stars caused by attractive self-interaction of the axionlike particles and find that these processes proceed in an unexpected universal way. First, nonlinear self-similar evolution (called "wave collapse" in condensed matter physics) forces the particles to fall into the star center. Second, interactions in the dense center create an outgoing stream of mildly relativistic particles which carries away an essential part of the star mass. The collapse stops when the star remnant is no longer able to support the self-similar infall feeding the collisions. We shortly discuss possible astrophysical and cosmological implications of these phenomena.

Universal properties of dark matter halos.

We discuss the universal relation between density and size of observed dark matter halos that was recently shown to hold on a wide range of scales, from dwarf galaxies to galaxy clusters. Predictions of cold dark matter (ΛCDM) N-body simulations are consistent with this relation. We demonstrate that this property of ΛCDM can be understood analytically in the secondary infall model. Qualitative understanding given by this model provides a new way to predict which deviations from ΛCDM or large-scale modifications of gravity can affect universal behavior and, therefore, to constrain them observationally.

Strategy for searching for a dark matter sterile neutrino.

We propose a strategy for how to look for dark matter particles possessing a radiative decay channel and derive constraints on their parameters from observations of x rays from our own Galaxy and its dwarf satellites. When applied to sterile neutrinos in the keV mass range this approach gives a significant improvement to restrictions on neutrino parameters compared with previous works.

Quantum cosmology of the brane universe.

We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-de Sitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial conditions, is conceptually more simple than in the (3+1)-dimensional case. The Wheeler-DeWitt equation is a finite-difference equation. It is exactly solvable in the case of a flat universe and we find the ground state of the system. The closed brane universe can be created as a result of decay of the bulk black hole.

Massive graviton as a testable cold-dark-matter candidate.

We construct a consistent model of gravity where the tensor graviton mode is massive, while linearized equations for scalar and vector metric perturbations are not modified. The Friedmann equation acquires an extra dark-energy component leading to accelerated expansion. The mass of the graviton can be as large as approximately (10(15) cm)(-1), being constrained by the pulsar timing measurements. We argue that nonrelativistic gravitational waves can comprise the cold dark matter and may be detected by the future gravitational wave searches.

Dynamics of symmetry breaking and tachyonic preheating.

We reconsider the old problem of the dynamics of spontaneous symmetry breaking (SSB) using 3D lattice simulations. We develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that SSB typically completes within a single oscillation as the field rolls towards the minimum of its effective potential. We show that, contrary to previous expectations, preheating in hybrid inflation is typically tachyonic. Our results may also be relevant for the theory of the formation of topological defects and of disoriented chiral condensates in heavy ion collisions.

Statistics of clustering of ultrahigh energy cosmic rays and the number of their sources.

Observation of clustering of ultrahigh energy cosmic rays (UHECR) suggests that they are emitted by compact sources. Assuming small ( <3 degrees ) deflection of UHECR during the propagation, the statistical analysis of clustering allows an estimate of the spatial density of the sources h(*), including those not yet observed. When applied to astrophysical models involving extragalactic sources, the estimate based on 14 events with energy E>10(20) eV gives h(*) approximately 6x10(-3) Mpc(-3). With increasing statistics, this estimate may lead to exclusion of some models.