Cosmic no-hair theorems and inflation

Abstract

An exact power-law inflationary solution possessing an exponential potential is given. We note that recent attempts to prove cosmic no-hair theorems for cosmological inflation exclude a wide range of ever-expanding cosmological models by the assumptions that positive spatial curvature implies the recopllpse of closed universes. Examples are given to show that, contrary to previous expectations, perfect fluid cosmologies with p = ( γ−1) ϵ need not approach isotropy and homogeneity as t→∞ for any constant γ > 0. The relevance to the problem of closed universes which recollapse before inflation occurs is also discussed.