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Asymptotic self-similarity breaking at late times in cosmology

J. Wainwright·M. J. Hancock·C. Uggla
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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 $γ$ satisfies $γ\leq 4/3$ 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.

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J. Wainwright, M. J. Hancock, C. Uggla. 1998-12-02. Asymptotic self-similarity breaking at late times in cosmology. https://doi.org/10.1088/0264-9381%2F16%2F8%2F302

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