Case for an EeV Gravitino

We consider the possibility that supersymmetry is broken above the inflationary mass scale and that the only "low" energy remnant of supersymmetry is the gravitino with a mass of the order of the EeV scale. The gravitino in this class of models becomes a candidate for the dark matter of the Universe. To avoid the overproduction of gravitinos from the decays of the next-to-lightest supersymmetric particle we argue that the supersymmetric spectrum must lie above the inflationary mass scale (M_{SUSY}>10^{-5}M_{P}∼10^{13}  GeV). Since m_{3/2}≃M_{SUSY}^{2}/M_{P}, we expect m_{3/2}≳0.2  EeV. Cosmological constraints then predict a relatively large reheating temperature between 10^{10} and 10^{12}  GeV.