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 ∼10−2M3 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 epochʹ 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.