Cosmic no-hair theorem in homogeneous spacetimes. I. Bianchi models

Extending the proof of the cosmic no-hair theorem for Bianchi models in power-law inflation, the authors prove a more general cosmic no-hair theorem for all 0<or= lambda < square root 2, where lambda is the coupling constant of an exponential potential of an inflaton phi , exp(- lambda kappa phi ). For any initially expanding Bianchi-type model except type IX, they find that the isotropic inflationary solution is the unique attractor and that anisotropies always enhance inflation. For Bianchi IX, this conclusion is also true, if the initial ratio of the vacuum energy Lambda _eff to the maximum 3-curvature ⁽³⁾R_max is larger than 1/(3(1- lambda ²/2)) and its time derivative is initially positive. It turns out that the sufficient condition for inflation in Bianchi type=IX spacetimes with cosmological constant Lambda , which is a special case of the theorem ( lambda =0) become less restrictive than Wald's one (1984). For type IX, they also show a recollapse theorem.