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We investigate supergravity models in which the lightest supersymmetricparticle (LSP) is a stable gravitino. We assume that the next-lightest supersymmetricparticle (NLSP) freezes out with its thermal relic density before decayingto the gravitino at time t10^4-10^8s. In contrast to studies that assume a fixed gravitino relic density, the thermalrelic density assumption implies upper, not lower, bounds on superpartnermasses, with important implications for particle colliders. We consider slepton, sneutrino, and neutralino NLSPs, and determine what superpartner masses areviable in all of these cases, applying cosmic microwave background (CMB) andelectromagnetic and hadronic big bang nucleosynthesis (BBN) constraints tothe leading two- and three-body NLSP decays. Hadronic constraints have beenneglected previously, but we find that they provide the most stringent constraintsin much of the natural parameter space. We then discuss the collider phenomenologyof supergravity with a gravitino LSP. We find that colliders may provide importantinsights to clarify BBN and the thermal history of the Universe below temperaturesaround 10 GeV and may even provide precise measurements of thegravitino's mass and couplings.
Feng et al. (Mon,) studied this question.