Searcharxiv⌕ Search

arXiv subjects

I. M. Khalatnikov

Publications and source records attributed to I. M. Khalatnikov.

15 recordsLinked to original sources
arXiv2019

Quasi-isotropic expansion for a two-fluid cosmological model containing radiation and string gas

The quasi-isotropic expansion for a simple two-fluid cosmological model, including radiation and string gas is constructed. The first non-trivial order expressions for the metric coefficients, energy densities and velocities are explicitly written down. Their small and large time asymptotics are studied. It is found that the large time asymptotic for the anisotropic component of the metric coefficients grows faster than that of the isotropic (trace-proportional) component.

astro-ph.CO↗
arXiv2015

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.

gr-qc↗
arXiv2008

Lev Landau and the problem of singularities in cosmology

We consider different aspects of the problem of cosmological singularity such as the BKL oscillatory approach to singularity, the new features of the cosmological dynamics in the neighbourhood of the singularity in multidimensional and superstring cosmological models and their connections with such a modern branch of mathematics as infinite-dimensional Lie algebras. Besides, we consider some new types of cosmological singularities which were widely discussed during last decade after the discovery of the phenomenon of cosmic acceleration.

gr-qc↗
arXiv2003

Quasi-isotropic solution of the Einstein equations near a cosmological singularity for a two-fluid cosmological model

The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized to the case of a two-fluid cosmological model. This solution describes non-decreasing modes of adiabatic and isocurvature scalar perturbations and gravitational waves in the regime when deviations of a space-time metric from the homogeneous isotropic Friedmann-Robertson-Walker (FRW) background are large while locally measurable quantities like Riemann tensor components are still close to their FRW values. The general structure of the perturbation series is presented and the first coefficients of the series expansion for the metric tensor and the fluid energy densities and velocities are calculated explicitly.

gr-qc↗
arXiv2003

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 solutions

gr-qc↗
arXiv2002

Comment about quasi-isotropic solution of Einstein equations near cosmological singularity

We generalize for the case of arbitrary hydrodynamical matter the quasi-isotropic solution of Einstein equations near cosmological singularity, found by Lifshitz and Khalatnikov in 1960 for the case of radiation-dominated universe. It is shown that this solution always exists, but dependence of terms in the quasi-isotropic expansion acquires a more complicated form.

gr-qc↗
arXiv2000

Diagram technique for perturbation theory calculations of the effective conductivity of two-dimensional systems

The perturbation theory for calculation of the effective conductivity of the plane consisting of pieces of different conductivities is constructed and the convenient diagram technique for this perturbation theory is elaborated. It is shown that for the chessboard perturbative calculations give results which are in agreement with the well-known formula $σ_{eff} = \sqrt{σ_1σ_2}$. The components of the tensor of effective conductivity for the anisotropic three-color chessboard are calculated. It is shown that the isotropic (symmetric) part of effective conductivity calculated up to the sixth order of perturbation theory satisfies the Bruggeman effective medium equation for symmetric three-color structures with equally partitioned components. We also consider isotropic three-color chessboard with nonequal weights of colors. In this case the perturbation theory already in fourth order contradicts the results following from the Bruggeman equation for nonequal weights.

cond-mat.mtrl-sci↗
arXiv1998

Instability and Chaos in Non-Linear Wave Interaction: a simple model

We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above which a loss of stability appears. The dependence of the critical input power on the physical parameters is analyzed. For a driving force with higher amplitude chaotic behavior is observed. Generalization to interactions which include higher modes is discussed. Keywords: Non-Linear Waves, Stability, Chaos.

chao-dyn↗
arXiv1998

Comment about UV regularization of basic commutators in string theories

Recently proposed by Hwang, Marnelius and Saltsidis zeta regularization of basic commutators in string theories is generalized to the string models with non-trivial vacuums. It is shown that implementation of this regularization implies the cancellation of dangerous terms in the commutators between Virasoro generators, which break Jacobi identity.

hep-th↗
arXiv1998

Simplest cosmological model with the scalar field II. Influence of cosmological constant

Continuing the investigation of the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity we study an influence of the cosmological constant on the behaviour of trajectories in closed minisuperspace Friedmann-Robertson-Walker model. The transition from chaotic to regular behaviour for large values of cosmological constant is discussed. Combining numerical calculations with qualitative analysis both in configuration and phase space we present a convenient classification of trajectories.

gr-qc↗
arXiv1998

Simplest cosmological model with the scalar field

We investigate the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity. The classification of trajectories in closed minisuperspace Friedmann-Robertson-Walker model is presented.The fractal nature of a set of infinitely bounced trajectories is discussed. The results of numerical calculations are compared with those obtained byperturbative analytical calculations around the exactly solvable minisuperspace cosmological model with massless scalar field.

gr-qc↗
arXiv1998

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.

gr-qc↗
arXiv1995

Non-minimally coupled complex scalar field in classical and quantum cosmology

We investigate the cosmological model with 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. These solutions give a rather non-trivial examples of real tunnelling geometries. Possible interpretation of obtained results and their connection with inflationary cosmology is discussed.

gr-qc↗