We show that the isocurvature perturbations imply that the gravitationally produced superheavy dark matter must have masses larger than a few times the Hubble expansion rate at the end of inflation. This together with the bound on tensor to scalar contribution to the CMB induces a lower bound on the reheating temperature for superheavy dark matter to be about ${10}^7\mathrm{GeV}$. Hence, if the superheavy dark-matter scenario is embedded in supergravity models with gravity mediated supersymmetry breaking, the gravitino bound will squeeze this scenario. Furthermore, the CMB constraint strengthens the statement that a gravitationally produced superheavy dark-matter scenario prefers a relatively large tensor mode amplitude if the reheating temperature must be less than ${10}^9\mathrm{GeV}$.

• Received 17 November 2004

DOI:https://doi.org/10.1103/PhysRevD.72.023511