  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 mass of order the EeV scale. The gravitino in this class
of models becomes a candidate for the dark matter of the Universe. To avoid the
over-production 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 ($M_{\rm SUSY} > 10^{-5} M_{\rm P} \sim
10^{13}$ GeV). Since $m_{3/2} \simeq M_{\rm SUSY}^2/M_{\rm P}$, we expect
$m_{3/2} \gtrsim 0.2$ EeV. Cosmological constraints then predict a relatively
large reheating temperature between $10^{10}$ and $10^{12}$ GeV.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena;High Energy Physics - Theory