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

TL;DR

This paper investigates the behavior of inhomogeneities in the metric near a cosmological singularity in multidimensional Einstein gravity, revealing a billiard-like dynamics with statistical properties and the influence of scalar fields.

Contribution

It provides a detailed analysis of inhomogeneous solutions near singularities, characterizing their dynamics as a finite-volume billiard and deriving an invariant measure for inhomogeneity statistics.

Findings

Metric inhomogeneities follow a billiard dynamics near singularity.

The billiard has finite volume and is mixing, allowing statistical description.

Scalar fields influence the dynamics of inhomogeneities.

Abstract

The problem of construction of a general ihomogeneous solution of $D$-dimensional Einstein equations in the vicinity of a cosmological singularity is considered. It is shown that near the singularity a local behavior of metric functions is described by a billiard on a space of a constant negative curvature. The billiard is shown to have a finite volume and consequently to be a mixing one. Dynamics of inhomogeneities of metric is studied and it is shown that its statistical properties admit a complete description. An invariant measure describing statistics of inhomogeneities is obtained and a role of a minimally-coupled scalar field in dynamics of the inhomogeneities is also considered.