Constraint on the gravitino mass in hybrid inflation

We revisit the F-term hybrid inflation model in supergravity. In particular, we point out that a constant term in the superpotential has significant effects on the inflaton dynamics. It is shown that the hybrid inflation model suffers from several potential problems: tuning of the initial condition, gravitino overproduction and formation of cosmic strings, for both minimal and non-minimal Kähler potentials. These problems can only be avoided in gauge-mediated SUSY breaking models where the gravitino is relatively light and the constant term in the superpotential is not important. Implications on the non-thermal leptogenesis scenario are also described