We investigate the constraint on the abundance of primordial black holes ( PBHs ) and the spectral index n of primeval 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 primeval density perturbations should be n < 1.27 .
Since the universe is still optical thick at the reionization redshift z \sim 6 - 8 , this constraint is independent of the unknown parameter of reheating temperature of the inflation .
The ionizing photon background from the PBHs can be well approximated by a power law spectrum J ( \nu ) \propto { \nu } ^ { 3 } , which is greatly different from those given by models of massive stars and quasars .