Gravitino dark matter in gravity mediation

We study general conditions for the gravitino to be the lightest supersymmetric particle (LSP) in models with gravity mediated supersymmetry breaking. We find that the decisive quantities are the Kähler potential K and the gauge kinetic function f. In constrained MSSM (CMSSM) type models, the gravitino LSP occurs if the gaugino mass at the GUT scale is greater than approximately 2.5 gravitino masses. This translates into K″/f′<0.2, where the derivatives are taken with respect to the dominant SUSY breaking field. This requirement can easily be satisfied in string-motivated setups.