A generalisation of the Heckmann - Schucking cosmological solution

An exact solution of the Einstein equations for a Bianchi -I universe in the presence of dust, stiff matter and cosmological constant, generalising the well-known Heckmann-Schucking solution is presented. PACS: 04.20-q; 04.20.Dw Keywords: Exact cosmological solutionsComment: LaTeX file, 10 pages. Physics Letters B, to appea

Relativistic hodograph equation for a two-dimensional stationary isentropic hydrodynamical motion

We derive a relativistic hodograph equation for a two-dimensional stationary isentropic hydrodynamical motion. For the case of stiff matter, when the velocity of sound coincides with the light speed, the singularity in this equation disappears and the solutions become regular in all hodograph plane.Comment: 5 page

Binary Quantum Turbulence Arising from Countersuperflow Instability in Two-Component Bose-Einstein Condensates

We theoretically study the development of quantum turbulence from two counter-propagating superfluids of miscible Bose-Einstein condensates by numerically solving the coupled Gross-Pitaevskii equations. When the relative velocity exceeds a critical value, the counter-superflow becomes unstable and quantized vortices are nucleated, which leads to isotropic quantum turbulence consisting of two superflows. It is shown that the binary turbulence can be realized experimentally in a trapped system.Comment: 5 pages, 3 figure

Topological entropy for some isotropic cosmological models

The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be easily generalized for wide class of models. Different methods of calculation of topological entropy are compared.Comment: Final version to appear in Phys. Rev D. Minor changes, typos corrected; 29 pages with 2 eps figure

Stochastic cosmology, theories of perturbations and Lifshitz gravity

We review some works of E M Lifshitz connected with gravity and cosmology and also some later works, connected with his ideas. The main topics of this review are the stochastic cosmology of an anisotropic universe and of an isotropic universe with the scalar field, the quasi-isotropic (gradient) expansion in cosmology and Horava-Lifshitz gravity and cosmology.Comment: 30 pages, to appear in Physics - Uspekhi. arXiv admin note: text overlap with arXiv:0901.3775 by other author

Study on Two Coupled Relativistic Superfluids with Spontaneous Symmetry Breaking

In this paper, we have studied two coupled relativistic superfluids with spontaneous U(1) symmetry breaking, using Poisson bracket technique. After constructing the commutators between thermo-quantities and field quantities, the equations of motion are obtained. These equations describe the system in the frame of two-constituent superfluid theory and provide a clear picture relating the symmetry breaking and the physical quantities explicitly. The interference effect is discussed and the Josephson-type equation is also given. Furthermore, the dissipation effect and entropy production mechanism are presented and the dissipative coefficients are given explicitly in the first-order theory framework.Comment: 12 page

Dark Energy and Dark Matter unification via superfluid Chaplygin gas

A new model describing the dark sector of the universe is established. The model involves Bose-Einstein condensate (BEC) as dark energy (DE) and an excited state above it as dark matter (DM). The condensate is assumed to have a negative pressure and is embodied as an exotic fluid with Chaplygin equation of state. Excitations are described as a quasiparticle gas. It is shown that the model is not in disagreement with the current observations of the cosmic acceleration. The model predicts increase of the effective cosmological constant and a complete disappearance of the matter at the far future.Comment: 13 pages, 3 figure

Complex inflaton field in quantum cosmology

We investigate the cosmological model with the complex scalar self-interacting inflaton field non-minimally coupled to gravity. The different geometries of the Euclidean classically forbidden regions are represented. The instanton solutions of the corresponding Euclidean equations of motion are found by numerical calculations supplemented by the qualitative analysis of Lorentzian and Euclidean trajectories. The applications of these solutions to the no-boundary and tunneling proposals for the wave function of the Universe are studied. Possible interpretation of obtained results and their connection with inflationary cosmology is discussed. The restrictions on the possible values of the new quasi-fundamental constant of the theory-non-zero classical charge-- are obtained. The equations of motion for the generalized cosmological model with complex scalar field are written down and investigated. The conditions of the existence of instanton solutions corresponding to permanent values of an absolute value of scalar field are obtained.Comment: 34 pages with 2 gif figures, mprocl.sty, To appear in International Journal of Modern Physics