Supersymmetry and primordial black hole abundance constraints

We study the consequences of supersymmetry for primordial black hole (PBH) abundance constraints. PBHs will emit supersymmetric particles during their evaporation when their mass is less than about 10^11 g. In most models of supersymmetry the lightest of these particles, the lightest supersymmetric particle (LSP), is stable and will hence survive to the present day. We calculate the limit on the initial abundance of PBHs from the requirement that the present day LSP density be less than the critical density. We apply this limit, along with those previously obtained from the effects of PBH evaporation on nucleosynthesis and the present day density of PBHs, to PBHs formed from the collapse of inflationary density perturbations in the context of supersymmetric inflation models. If the reheat temperature after inflation is low, so as to avoid the overproduction of gravitinos and moduli, then the lightest PBHs which are produced in significant numbers will be evaporating around the present day and there are therefore no constraints from the effects of the evaporation products on nucleosynthesis or from the production of LSPs. We then examine models with a high reheat temperature and a subsequent period of thermal inflation. In these models avoiding the overproduction of LSPs limits the abundance of low mass PBHs which were previously unconstrained. Throughout we incorporate the production, at fixed time, of PBHs with a range of masses, which occurs when critical collapse is taken into account.