The power-law dependence between the matter-radiation and Hubble anisotropies

Abstract

In this paper, we investigate the cosmological evolution of the Hubble and the matter-radiation anisotropies, characterized by [Formula: see text] and [Formula: see text], respectively, under the power-law condition [Formula: see text]. This is a suitable choice in order to understand how different [Formula: see text] and [Formula: see text] would behave in the expanding universe if they had distinct orders of magnitude. Hence, their early and late-time behaviors are examined, and in particular, the dependence of their qualitative features on [Formula: see text]. This includes some nontrivial aspects in their long-time dynamics, which goes beyond the reach of the linear perturbations of the homogeneous and isotropic models. Besides those cosmological concerns, the concept of anisotropy in general relativity and its counterpart in Einstein’s equations is clarified and interpreted, and the general notion of the Kasner plane, the arena where its dynamics takes place, is extended beyond the reach of the spatially homogeneous models.