Eluding the Gravitino Overproduction in Inflaton Decay
  It is known that gravitinos are non-thermally produced in inflaton decay processes, which excludes many inflation models for a wide range of the gravitino mass. We find that the constraints from the gravitino overproduction can be greatly relaxed if the supersymmetry breaking field is much lighter than the inflaton, and if the dynamical scale of the supersymmetry breaking is higher than the inflaton mass. In particular, we show that many inflation models then become consistent with the pure gravity mediation with O(100)TeV gravitino which naturally explains the recently observed Higgs boson mass of about 125GeV. 
Kazunori Nakayama, Fuminobu Takahashi, Tsutomu T. Yanagida
hep-ph astro-ph.CO hep-th