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 sqrt(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. © 2009 Elsevier B.V. All rights reserved.
Kersten, J., & Lebedev, O. (2009). Gravitino dark matter in gravity mediation. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 678(5), 481–484. https://doi.org/10.1016/j.physletb.2009.06.062