Asymptotic self-similarity breaking at late times in cosmology

TL;DR

This paper investigates the late-time behavior of Bianchi type VII$_0$ cosmological models, revealing a novel Weyl curvature dominance and symmetry breaking that influence isotropization, with implications for more general cosmological models.

Contribution

It demonstrates that Bianchi VII$_0$ models experience a unique form of self-similarity breaking affecting late-time isotropization and introduces the concept of Weyl curvature dominance in these models.

Findings

Bianchi VII$_0$ models break self-similarity at late times.

Weyl curvature dominates the dynamics at late times.

Implications extend to more general cosmological models.

Abstract

We study the late time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII$_0$ with a perfect fluid source. We show that, in contrast to models of Bianchi type VII$_h$ which are asymptotically self-similar at late times, Bianchi VII$_0$ models undergo a complicated type of self-similarity breaking. This symmetry breaking affects the late time isotropization that occurs in these models in a significant way: if the equation of state parameter $\gamma$ satisfies $\gamma \leq 4/3$ the models isotropize as regards the shear but not as regards the Weyl curvature. Indeed these models exhibit a new dynamical feature that we refer to as Weyl curvature dominance: the Weyl curvature dominates the dynamics at late times. By viewing the evolution from a dynamical systems perspective we show that, despite the special nature of the class of models under consideration, this behaviour has implications for more general models.