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