Asymptotic self-similarity breaking at late times in cosmology

Abstract

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