# 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.

## Key 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.