2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/40196Present data require a spectral index $n\gsim 0.95$ at something like 1-$σ$ level. If this lower bound survives it will constrain `new' and `modular' inflation models, while raising it to 1.00 would rule out all of these models plus many others. After inflation, gravitinos are created by the oscillating field until the `intermediate' epoch when the Hubble parameter falls below the gravitino mass, or reheating, whichever is earlier. In a wide range of parameter space, these gravitinos are more abundant than those from thermal collisions, leading to stronger cosmological constraints.Updated version of a talk at COSMO2K, to appear in the proceedingsHigh Energy Physics - Phenomenologytext