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

In 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 most 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 (Roszkowski et al 2005 J. High. Energy Phys. JHEP08(2005)080) 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 m_{\widetilde {G}} in the GeV to TeV range, and for natural ranges of other supersymmetric parameters, the neutralino region is excluded, except for rather exceptional cases, while for smaller values of m_{\widetilde {G}} 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 m_{\widetilde {G}} , a large enough reheating temperature. If m_{\widetilde {G}}\gt 1~\mathrm

{GeV} then T_R > 10⁸ GeV, if allowed by BBN and other constraints but, for light gravitinos, if m_{\widetilde

{G}}\gt 100~\mathrm {keV} then T_R > 3 × 10³ GeV. On the other hand, constraints mostly from BBN imply an upper bound T_{\mathrm

{R}}\lesssim 4\times 10^9~\mathrm {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.