Dynamics of inhomogeneities of the metric in the vicinity of a singularity in multidimensional cosmology

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Abstract
The dynamics and properties of large-scale inhomogeneities of the metric in the general solution to the D-dimensional Einstein equations with any matter sources satisfying the inequality ε≥p in the vicinity of a cosmological singularity are considered. It is shown that near the singularity the local behavior of a part of the metric functions is described by a billiard on a space of constant negative curvature. If D≤10, the billiard has a finite volume and shows stochastic properties. This stochasticity results in the increasing of the degree of inhomogeneity of that part of the dynamical functions and leads to the formation of spatial chaos. For this case the dynamics of the inhomogeneities of the metric is studied and it is shown that the Universe acquires a quasi-isotropic character. The invariant measure describing the statistics of inhomogeneities is obtained and the role of a minimally coupled scalar field in the dynamics of inhomogeneities is also considered. The results obtained may be used for a more adequate description of processes at the early stages of the Universe, i.e., in solving problems of realistic cosmological scenarios, studying the role of quantum effects in cosmology, initial data problem, and the formation of structures in the Universe.
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