  Motivated by the absence of signals of new physics in both searches for new
particles at LHC and for a Weakly Interacting Massive Particle (WIMP) dark
matter candidate, we consider a scenario where supersymmetry is broken at a
scale above the reheating temperature. The low energy particle content consists
then only in Standard Model states and a gravitino. We investigate the
possibility that the latter provides the main component of dark matter through
a freeze in mechanism from annihilation of thermalized Standard Model
particles. We focus on the case where its production through scattering in the
thermal plasma is well approximated by the non-linear supersymmetric effective
Lagrangian of the associated goldstino and identify the parameter space allowed
by the cosmological constraints, allowing the possibility of large reheating
temperature compatible with leptogenesis scenarios, alleviating the so called
"gravitino problem".
