Constraints on Primordial Black Holes and Primordial Density Perturbations from the Epoch of Reionization

Abstract

We investigate the constraints on the abundance of primordial black holes (PBHs) and the spectral index n of primordial density perturbations given by the ionizing photon background at the epoch of reionization. Within the standard inflationary cosmogony, we show that the spectral index n of the power-law power spectrum of primordial density perturbations should be n < 1.27. Since the universe is still optically thick at the reionization redshift z ∼ 6-8, this constraint is independent of the unknown parameter of the reheating temperature of the inflation. The ionizing photon background from the PBHs can be well approximated by a power-law spectrum J(v) ∞ v 3, which differs greatly from those given by models of massive stars and quasars.