Perturbative Reheating and Gravitino Production in Inflationary Models

The low reheat temperature at the end of inflation from the gravitino bound constrains the creation of heavy Majorana neutrinos associated with models of leptogenesis. However, a detailed view of the reheating of the Universe at the end of inflation implies that the maximum temperature during reheating, $\Tmax$, can be orders of magnitude higher than the final reheat temperature. This then allows for the production of the heavy Majorana neutrinos needed for leptogenesis. We carry out the complementary calculation of the gravitino production during reheating and its dependence on $\Tmax$. We find that the gravitino abundance generated during reheating for a quartic potential is comparable to the standard estimate of the abundance generated after reheating and study its consequences for leptogenesis.