Linearization of homogeneous, nearly-isotropic cosmological models

Abstract

Homogeneous, nearly-isotropic Bianchi cosmological models are considered. Their time evolution is expressed as a complete set of non-interacting linear modes on top of a Friedmann–Robertson–Walker background model. This connects the extensive literature on Bianchi models with the more commonly-adopted perturbation approach to general relativistic cosmological evolution. Expressions for the relevant metric perturbations in familiar coordinate systems can be extracted straightforwardly. Amongst other possibilities, this allows for future analysis of anisotropic matter sources in a more general geometry than usually attempted. We discuss the geometric mechanisms by which maximal symmetry is broken in the context of these models, shedding light on the origin of different Bianchi types. When all relevant length scales are super-horizon, the simplest Bianchi I models emerge (in which anisotropic quantities appear parallel transported). Finally we highlight the existence of arbitrarily long near-isotropic epochs in models of general Bianchi type (including those without an exact isotropic limit).