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 ∼ 10M 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 latetime 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. Introduction Gravitinos are created in the early Universe by thermal collisions [1], and some time ago [2] it was pointed out that they will also be created non-thermally, starting from the vacuum fluctuation that exists well before horizon exit during inflation. To see whether creation from the vacuum is significant, one needs equations which describe the evolution of the gravitino mode functions. Such equations have recently been presented [3, 4], for the case that only one chiral superfield is relevant. Using them, the authors find that the number density of gravitinos created just after inflation is of order 10M, where M is the mass of the inflaton after inflation, and they have noted that these gravitinos may be more abundant after reheating than those created from thermal collisions. A similar result has been obtained for hybrid inflation, which involves at least two fields, assuming that in this context the gravitino becomes the goldstino of global supersymmetry [5] (see also [6]). In this note, we argue that this is unlikely to be the end of the story [7]. Rather, creation is likely to continue, maintaining about the same number density, until either the ‘intermediate epoch’ when Hubble parameter falls below the gravitino mass, or the reheat epoch if that occurs earlier. We begin by verifying that such late-time creation