Supersymmetric and smooth hybrid inflation in the light of WMAP3

In their minimal form both supersymmetric and smooth hybrid inflation yield a scalar spectral index ns close to 0.98, to be contrasted with the result ns=0.951-0.019+0.015 from WMAP3. To realize better agreement, following Bastero-Gil, King, and Shafi, we extend the parameter space of these models by employing a nonminimal Kaehler potential. We also discuss nonthermal leptogenesis by inflaton decay and obtain new bounds in these models on the reheat temperature to explain the observed baryon asymmetry