Cosmological gravitino problem confronts electroweak physics

A generic feature of gauge-mediated supersymmetry breaking models is that the gravitino is the lightest supersymmetric particle (LSP). In order not to overclose the universe, the gravitino LSP should be light enough (~ 1 keV), or appropriately heavy (~ 1 GeV). We study further constraints on the mass of the gravitino imposed by electroweak experiments, i.e., muon g-2 measurements, electroweak precision measurements, and direct searches for supersymmetric particles at LEP2. We find that the heavy gravitino is strongly disfavored from the lower mass bound on the next-to-LSP. The sufficiently light gravitino, on the other hand, has rather sizable allowed regions in the model parameter space.