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We investigate gravitino dark matter produced thermally at high temperaturesand in decays of a long-lived sneutrino. We consider the Non-Universal HiggsModel and a generalized gauge mediation model, and in each case identifysneutrino LOSP regions of the parameter space consistent with the mass of theHiggs-like boson observed at the LHC. We apply relevant collider andcosmological bounds, including constraints from Big Bang Nucleosynthesis andfrom warm dark matter on large scale structures. Generally, we find allowedvalues of the reheating temperature TR below 10^9 GeV, i.e. somewhat smallerthan the values needed for thermal leptogenesis, even with a conservative lowerbound of 122 GeV on the Higgs mass. Requiring mass values closer to 126 GeVimplies TR below 10^7 GeV and the gravitino mass less than 10 GeV.

Gravitino dark matter with constraints from Higgs boson mass and sneutrino decays