Asymptotic isotropization in inhomogeneous cosmology

In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium state at late times, and near the flat FL equilibrium state at early times. Our results show that there exists an open set of solutions approaching the de Sitter state at late times, consistent with the cosmic no-hair conjecture. On the other hand, solutions that approach the flat FL state at early times are special and admit a so-called isotropic initial singularity. For both classes of models the asymptotic expansion of the line element contains an arbitrary spatial metric at leading order, indicating asymptotic spatial inhomogeneity. We show, however, that in the asymptotic regimes this spatial inhomogeneity is significant only at super-horizon scales.