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We show that the isocurvature perturbations imply that the gravitationallyproduced superheavy dark matter must have masses larger than few times theHubble expansion rate at the end of inflation. This together with the bound ontensor to scalar contribution to the CMB induces a lower bound on the reheatingtemperature for superheavy dark matter to be about 10^7 GeV. Hence, if thesuperheavy dark matter scenario is embedded in supergravity models with gravitymediated SUSY breaking, the gravitino bound will squeeze this scenario.Furthermore, the CMB constraint strengthens the statement that gravitationallyproduced superheavy dark matter scenario prefers a relatively large tensor modeamplitude if the reheating temperature must be less than 10^9 GeV.Comment: 29 pages, 2 figure

Isocurvature constraints on gravitationally produced superheavy dark matter