Late-time asymptotic dynamics of Bianchi VIII cosmologies

TL;DR

This paper rigorously describes the late-time behavior of Bianchi VIII cosmologies, revealing asymptotic self-similarity breaking and Weyl curvature dominance, with detailed expansions of physical variables.

Contribution

It provides the first complete description of late-time evolution for Bianchi VIII models, including asymptotic expansions and the phenomenon of Weyl curvature dominance.

Findings

Asymptotic self-similarity breaks down at late times.

Hubble-normalized Weyl curvature diverges, indicating Weyl dominance.

Models exhibit specific limiting behaviors characterized by asymptotic expansions.

Abstract

In this paper we give, for the first time, a complete description of the late-time evolution of non-tilted spatially homogeneous cosmologies of Bianchi type VIII. The source is assumed to be a perfect fluid with equation of state $p = (\gamma - 1)\mu$, where $\gamma$ is a constant which satisfies $1 \leq \gamma \leq 2$. Using the orthonormal frame formalism and Hubble-normalized variables, we rigorously establish the limiting behaviour of the models at late times, and give asymptotic expansions for the key physical variables. The main result is that asymptotic self-similarity breaking occurs, and is accompanied by the phenomenon of `Weyl curvature dominance', characterized by the divergence of the Hubble-normalized Weyl curvature at late times.