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24 pagesIn the framework of the Constrained MSSM we re--examine the gravitino as the lightest superpartner and a candidate for cold dark matter in the Universe. Unlike in other recent studies, we include both a thermal contribution to its relic population from scatterings in the plasma and a non--thermal one from neutralino or stau decays after freeze--out. Relative to a previous analysis [1] we update, extend and considerably improve our treatment of constraints from observed light element abundances on additional energy released during BBN in association with late gravitino production. Assuming the gravitino mass in the GeV to TeV range, and for natural ranges of other supersymmetric parameters, the neutralino region is excluded, while for smaller values of the gravitino mass it becomes allowed again. The gravitino relic abundance is consistent with observational constraints on cold dark matter from BBN and CMB in some well defined domains of the stau region but, in most cases, only due to a dominant contribution of the thermal population. This implies, depending on the gravitino mass, a large enough reheating temperature. If $\mgravitino>1$ GeV then $T_R>10^8$ GeV, if allowed by BBN and other constraints but, for light gravitinos, if $\mgravitino>100$ keV then $T_R>3\times 10^3$ GeV. On the other hand, constraints mostly from BBN imply an upper bound $T_Rlsim4\times10^9$ GeV which is marginally consistent with thermal leptogenesis. Finally, most of the preferred stau region corresponds to the physical vacuum being a false vacuum. The scenario can be partially probed at the LHC

Gravitino dark matter in the constrained minimal supersymmetric standard model with improved constraints from big bang nucleosynthesis