Gravitino-overproduction problem in an inflationary universe

We show that the gravitino-overproduction problem is prevalent among inflation models in supergravity. An inflaton field generically acquires (effective) nonvanishing auxiliary field GΦ(eff), if the Kähler potential is nonminimal. The inflaton field then decays into a pair of the gravitinos. We extensively study the cosmological constraints on GΦ(eff) for a wide range of the gravitino mass. For many inflation models we explicitly estimate GΦ(eff), and show that the gravitino-overproduction problem severely constrains the inflation models, unless such an interaction as K=κ/2| |2z2+H.c. is suppressed (here z is the field responsible for the supersymmetry breaking). We find that many of them are already excluded or on the verge of, if κ∼O(1).