COSMIC NO-HAIR THEOREM IN HOMOGENEOUS SPACETIMES .1. BIANCHI MODELS

Extending our recent proof of the cosmic no-hair theorem for Bianchi models in power-law inflation, we prove a more general cosmic no-hair theorem for all 0 less-than-or-equal-to lambda < square-root 2, where lambda is the coupling constant of an exponential potential of an inflaton phi, exp(-lambdakappaphi). For any initially expanding Bianchi-type model except type IX, we 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 - lambda2/2)] 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), becomes less restrictive than Wald's one. For type IX, we also show a recollapse theorem.