  Gravitinos are expected to be produced in any local supersymmetric model.
Using their abundance prediction as a function of the reheating energy scale,
it is argued that the next generation of Cosmic Microwave Background
experiments could exclude supergravity or strongly favor "thermal-like"
inflation models if B mode polarized radiation were detected. Galactic
cosmic--ray production by evaporating primordial black holes is also
investigated as a way of constraining the Hubble mass at the end of inflation.
Subsequent limits on the gravitino mass and on the related grand unification
parameters are derived.
