Kantowski–Sachs cosmological models approaching isotropy

Abstract

In this article we analyze a particular class of anisotropic cosmological models, the Kantowski–Sachs models, in the presence of a nonzero cosmological constant Λ. We study them qualitatively by means of autonomous systems with two and three dimensions. The plane autonomous system gives a new class of empty Kantowski–Sachs cosmologies, with Λ>0 and Λ<0. We find two new types of singularity points. The autonomous system with three dimensions yields a set of solutions of nonzero measure becoming isotropic in an infinite cosmological time.