Inflaton Decay in Supergravity and Gravitino Problem

We have recently shown that, if the inflaton has a nonzero vacuum expectation value, it generically couples to any matter fields that appear in the superpotential at the tree level, and to any gauge sectors through anomalies in the supergravity. Through these processes, the inflaton decays into the supersymmetry breaking sector, producing many gravitinos. The inflaton also directly decays into a pair of the gravitinos. Taking account of these processes, we derive constraints on both inflation models and supersymmetry breaking scenarios for avoiding overproduction of the gravitinos.