Forming sub-horizon black holes at the end of inflation

Abstract

Previous authors have calculated the mass function of primordial black holes only on scaleswhich are well outside the horizon at the end of inflation. Here we extend thecalculation to sub-horizon scales, on which the density perturbation never becomesclassical. Regarding the formation of black holes as a ‘measurement’ of the (highpeaks) of the density perturbation, we estimate a mass function by assumingthat black holes form as soon as inflation ends, in those rare regions where theBardeen potential exceeds a threshold value of Ψc ≃ 0.5.