Gravitino-overproduction problem in an inflationary universe

We show that the gravitino-overproduction problem is prevalent among inflation models in supergravity. An inflaton field φ generically acquires (effective) nonvanishing auxiliary field G_Φ⁽ᵉᶠᶠ⁾, if the K\"ahler potential is nonminimal. The inflaton field then decays into a pair of the gravitinos. We extensively study the cosmological constraints on G_Φ⁽ᵉᶠᶠ⁾ for a wide range of the gravitino mass. For many inflation models we explicitly estimate G_Φ⁽ᵉᶠᶠ⁾, and show that the gravitino-overproduction problem severely constrains the inflation models, unless such an interaction as K=κ/2|φ|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).