Cosmic no-hair theorems and inflation

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 assumption that positive spatial curvature implies the recollapse of closed universes. Examples are given to show that, contrary to previous expectations, perfect fluid cosmologies with p=(γ-1)element of 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. (orig.)