Gravitino production in hybrid inflationary models

It has been shown recently that it is possible to excite gravitinos in an expanding background due to a time-varying scalar field oscillating at the bottom of the inflationary potential. The two components of the gravitino, namely helicity $1/2$ and helicity $3/2,$ are excited differently due to the presence of different time-varying mass scales in the problem. In this paper we analyze the production of both the helicities in multichiral scenario, in particular focusing on a general model of hybrid inflation. Fermion production in hybrid models is very much different from that of the chaotic models discussed so far in the literature. In this paper we give a full account of gravitino production analytically and numerically. It is noticed that the creation of gravitinos does not take place in the first few oscillations of the inflaton field, rather the production is a gradual and delayed process. It takes roughly $30-40$ oscillations to build up production and for the saturation to take place it can even take longer depending on the model parameters. We give an estimation of the reheat temperature and a brief discussion of back reaction on the gravitino production which could change its abundance.