Asymptotic self-similarity breaking at late times in cosmology

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 VII0 with a perfect fluid source. We show that, in contrast to models of Bianchi type VIIh which are asymptotically self-similar at late times, Bianchi VII0 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 satisfies (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.