The Gravitino-Overproduction Problem in Inflationary Universe

We show that the gravitino-overproduction problem is prevalent among inflation models in supergravity. An inflaton field \phi generically acquires (effective) non-vanishing auxiliary field G_\phi, if the K\"ahler potential is non-minimal. The inflaton field then decays into a pair of the gravitinos. We extensively study the cosmological constraints on G_\phi for a wide range of the gravitino mass. For many inflation models we explicitly estimate G_\phi, and show that the gravitino-overproduction problem severely constrains the inflation models, unless such an interaction as K = \kappa/2 |\phi|^2 z^2 + 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 \kappa \sim O(1).