Successful supersymmetric inflation

We reconsider the problems of cosmological inflation in effective supergravity theories. We argue that an inflaton in a hidden sector is likely to yield, without fine tuning, an inflationary potential with an energy scale set by a stage of spontaneous symmetry breaking below the Planck scale. In the simplest such model, normalization to the amplitude of the primordial density perturbations inferred from COBE requires the inflationary scale to be about 3\times 10^{14} GeV, implying a reheat temperature of order 10^{5} GeV. This is below the upper limit derived from consideration of the thermal generation of unstable gravitinos and their effects on primordial nucleosynthesis, but high enough to allow baryogenesis after inflation. Such consistency requires that gravitational waves contribute negligibly to the observed anisotropy of the cosmic microwave background radiation. Other models, including chaotic inflation, violate the reheat bound and require additional physics structure to be viable. We also consider the problems associated with direct gravitino production through inflaton decay and with other weakly coupled sectors such as the moduli encountered in (compactified) string theories.