Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models

TL;DR

This paper explores the dynamics of Bianchi cosmological models with anisotropic matter, revealing conditions for non-recollapsing solutions and oscillatory behavior near singularities, thus highlighting the significant impact of matter anisotropy.

Contribution

It provides a comprehensive analysis of Bianchi types I, II, and IX with anisotropic matter, extending understanding beyond perfect fluids and vacuum models.

Findings

Existence of non-recollapsing solutions in Bianchi type IX with anisotropic matter.

Vlasov matter models exhibit oscillatory behavior near singularities.

Anisotropic matter significantly alters cosmological dynamics compared to perfect fluids.

Abstract

The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following: (i) There exist matter models, compatible with the standard energy conditions, such that solutions of Bianchi type IX (closed cosmologies) need not necessarily recollapse; there is an open set of forever expanding solutions. (ii) Generic type IX solutions associated with a matter model like Vlasov matter exhibit oscillatory behavior toward the initial singularity. This behavior differs significantly from that of vacuum/perfect fluid cosmologies; hence "matter matters". Finally, we indicate that our methods can probably be extended to treat a number of open problems, in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.