Cosmic no-hair theorem in power-law inflation.

Abstract

We prove a cosmic no-hair theorem for Bianchi models in power-law inflation. Provided that the potential of an inflaton $\ensuremath{\varphi}$ is $\mathrm{exp}(\ensuremath{-}{\ensuremath{\lambda}}_{\ensuremath{\kappa}\ensuremath{\varphi}})$ with $0\ensuremath{\le}\ensuremath{\lambda}<\sqrt{\frac{2}{3}}$, we find that the isotropic power-law solution is the unique attractor for any initially expanding Bianchi-type models except type IX. For Bianchi type IX, this conclusion is also true if the initial ratio of the vacuum energy to the maximum three-curvature is larger than one half.