Kantowski-Sachs universes and the cosmic no-hair conjecture.

Abstract

We address the generality of an inflationary scenario in initially expanding Kantowski-Sachs space-times with a positive cosmological constant $\ensuremath{\Lambda}$. From a qualitative analysis of the Einstein equations, we investigate the initial conditions that induce an evolution towards the de Sitter solution. It is shown that the majority of the Kantowski-Sachs universes asymptotically approach a de Sitter stage. A zero-probability class of solutions which recollapse constitutes the exception. Thus, we conclude that the cosmic no-hair conjecture is widely valid in these Kantowski-Sachs cosmologies.