Constraints on the primordial curvature perturbation from primordial black holes

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We calculate the constraints on the primordial curvature perturbation at the end of inflation fromthe present day abundance of primordial black holes (PBHs), as a function of the reheat temperatureTRH. We first extend recent work on the formation of PBHs on scales which remainwithin the horizon during inflation and calculate the resulting constraints on thecurvature perturbation. We then evaluate the constraint from PBHs that form,more conventionally, from super-horizon perturbations. The constraints apply forTRH<108 GeV and the inclusion of sub-horizon PBHs leads to a limit which is roughly three times tighterthan the bound from super-horizon PBHs.