Contribution of the Weyl tensor to R2 inflation.

Abstract

To study the generality of inflation from Lagrangians containing higher powers of curvature, the effects of the square of the Weyl tensor, ${C}^{2}\ensuremath{\equiv}{C}_{\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\gamma}\ensuremath{\delta}}{C}^{\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\gamma}\ensuremath{\delta}}$, on the ${R}^{2}$ inflationary scenario is considered. By examining the stability of radiation-dominated Robertson-Walker universes for small perturbations, the ${C}^{2}$ 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 ${R}^{2}$ 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 ${C}^{2}$ terms restricts the success of ${R}^{2}$ inflation.