Late-time creation of gravitinos from the vacuum

Starting with the vacuum fluctuation, it is known that gravitinos will be created just after inflation, with number density $\sim {10}^{-2}{M}^3$ where $M$ is the mass of the inflaton. Here, we argue that creation may be expected to continue, maintaining about the same number density, until a usually much later epoch. This epoch is either the `intermediate epoch’ when Hubble parameter falls below the gravitino mass, or the reheat epoch if that is earlier. We verify that such late-time creation indeed occurs if only a single chiral superfield is relevant, using the description of the helicity 1/2 gravitino provided recently by Kallosh et. al. (hep-th/9907124) and Giudice et. al. (hep-ph/9907510). Arguments are presented in favor of late-time creation in the general case. For the usual inflation models, $M$ is rather large and gravitinos from late-time creation are so abundant that a subsequent era of thermal inflation is needed to dilute them.