  This paper investigates the parameter space of theories with gauge mediated
supersymmetry breaking leading to gravitino (cold) dark matter with mass
m_{3/2}= 1keV - 10MeV. We pay particular attention to the cosmological role of
messenger fields. Cosmology requires that these messengers decay to the visible
sector if the lightest messenger mass M_X > 30TeV. We then examine the various
possible messenger number violating interactions allowed by the symmetries of
the theory and by phenomenology. Late messenger decay generally results in
entropy production hence in the dilution of pre-existing gravitinos. We find
that in SU(5) grand unification only specific messenger-matter couplings allow
to produce the required amount of gravitino dark matter particles. Gravitino
dark matter with the correct abundance is however expected in larger gauge
groups such as SO(10) for generic non-renormalizable messenger-matter
interactions and for arbritrarily high post-inflationary reheating
temperatures.
