Post-Inflationary Gravitino Production Revisited
  We revisit gravitino production following inflation. As a first step, we
review the standard calculation of gravitino production in the thermal plasma
formed at the end of post-inflationary reheating when the inflaton has
completely decayed. Next we consider gravitino production prior to the
completion of reheating, assuming that the inflaton decay products thermalize
instantaneously while they are still dilute. We then argue that instantaneous
thermalization is in general a good approximation, and also show that the
contribution of non-thermal gravitino production via the collisions of inflaton
decay products prior to thermalization is relatively small. Our final estimate
of the gravitino-to-entropy ratio is approximated well by a standard
calculation of gravitino production in the post-inflationary thermal plasma
assuming total instantaneous decay and thermalization at a time $t \simeq
1.2/\Gamma_\phi$. Finally, in light of our calculations, we consider potential
implications of upper limits on the gravitino abundance for models of
inflation, with particular attention to scenarios for inflaton decays in
supersymmetric Starobinsky-like models.
