The asymptotic regimes of tilted Bianchi II cosmologies

TL;DR

This paper provides a comprehensive analysis of the dynamics of tilted Bianchi type II cosmologies, revealing how tilt influences singularity behavior and isotropization depending on the fluid's equation of state.

Contribution

It offers the first complete description of tilted Bianchi II cosmologies, detailing how tilt affects stability and evolution for different fluid parameters.

Findings

Tilt destabilizes Kasner solutions unless the fluid is stiff.

Tilt leads to Mixmaster-like singularities when not stiff.

Tilt increases the likelihood of isotropization at intermediate times.

Abstract

In this paper we give, for the first time, a complete description of the dynamics of tilted spatially homogeneous cosmologies of Bianchi type II. The source is assumed to be a perfect fluid with equation of state $p = (\gamma -1) \mu$, where $\gamma$ is a constant. We show that unless the perfect fluid is stiff, the tilt destabilizes the Kasner solutions, leading to a Mixmaster-like initial singularity, with the tilt being dynamically significant. At late times the tilt becomes dynamically negligible unless the equation of state parameter satisfies $\gamma > {10/7}$. We also find that the tilt does not destabilize the flat FL model, with the result that the presence of tilt increases the likelihood of intermediate isotropization.