Inverted hybrid inflation as a solution to gravitino problems in gravity mediation

It was recently found that the decay of the inflaton and the supersymmetry breaking field produces many gravitinos in the gravity mediation scenario. These discoveries showed that many inflation models such as chaotic, (smooth) hybrid, topological, and new inflation models are disfavored. Under these circumstances we search for a successful inflation model and find that the inverted hybrid inflation models can solve the gravitino overproduction problem by their distinctive shape of the potential. Furthermore, we show that this inflation model simultaneously can explain the observed baryon asymmetry through the nonthermal leptogenesis and is consistent with the WMAP results, that is, n_s=0.951_-0.019^+0.015 and the negligible tensor to scalar ratio.