Gravitino dark matter in gauge mediated supersymmetry breaking

This paper investigates the parameter space of theories with gauge-mediated supersymmetry breaking leading to gravitino (cold) dark matter with mass m3/2~1 keV→10 MeV. 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 MX30 TeV. 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 preexisting 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 nonrenormalizable messenger-matter interactions and for arbitrarily high post-inflationary reheating temperatures.