CONTRIBUTION OF THE WEYL TENSOR TO R2 INFLATION

To study the generality of inflation from Lagrangians containing higher powers of curvature, the effects of the square of the Weyl tensor, C2 = C-alpha-beta-gamma-delta-C-alpha-beta-gamma-delta, on the R2 inflationary scenario is considered. By examining the stability of radiation-dominated Robertson-Walker universes for small perturbations, the C2 term is determined to enter with a negative coupling constant. Both analytical arguments and numerical methods are used to investigate the influence of the various derivatives of the anisotropy in a Bianchi type-I universe. While a small anisotropy only slightly modifies the standard R2 scenario, for sufficiently large anisotropy the universe cannot isotropize and recollapse subsequently ensues. The critical values at which this behavior occurs is estimated. Thus, the inclusion of C2 terms restricts the success of R2 inflation.