Evolution of initially contracting Bianchi Class A models in the presence of an ultra-stiff anisotropic pressure fluid

TL;DR

This paper investigates how ultra-stiff anisotropic pressures influence the approach to singularities or bounces in Bianchi type IX universes, challenging assumptions about isotropisation in cyclic cosmological models.

Contribution

It demonstrates that dominant anisotropic pressures prevent isotropisation, leading to anisotropic singularities or bounces, thus emphasizing the importance of anisotropic stresses in cyclic universe scenarios.

Findings

Anisotropic pressures dominate lead to anisotropic singularities.

Isotropisation does not occur when anisotropic pressures are sufficiently stiff.

Anisotropic stresses are crucial for understanding bounces and singularities in cyclic models.

Abstract

We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropisation on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialise to consider the closed Bianchi type IX universe and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate on approach to the singularity, it will be anisotropic. We include an isotropic ultra-stiff ghost fluid with negative energy density in order to create a cosmological bounce at finite volume in the absence of the anisotropic fluid. When the dominant anisotropic fluid is present it leads to an anisotropic cosmological singularity rather than an isotropic bounce. The inclusion of anisotropic stresses generated by collisionless particles in an anisotropically expanding universe is therefore essential for a full analysis of the consequences of a cosmological bounce or singularity in cyclic universes.