R2inflation in anisotropic universes

The evolution of Bianchi type-I and type-IX universes for a theory of gravity with an $\epsilon R^2$ term added to the usual Lagrangian is considered. As in the spatially flat Robertson-Walker case considered previously by others, inflation is found to occur. For any amount of initial anisotropy, the anisotropy decays quickly relative to the length of the inflationary epoch, and the amount of expansion is enhanced by the anisotropy. The exceptions are Bianchi type-IX universes near or at isotropy. In these cases a wide range of initial parameters causes the universe to recollapse, thus reducing the phase space in which inflation can occur. The diagonal metric is shown to be the most general form in the $R^2$ theory for both Bianchi type-I universes with a perfect fluid and vacuum Bianchi type-IX models.