Reionization of the Universe induced by Primordial Black Holes

In this paper I will discuss the possibility of a reionization of the Universe due to the photons emitted by evaporating primordial black holes (PBHs); this process should happen during the last stages of the PBHs life, when the particle emission is very intense. I will study the time evolution of the ionization degree x, of the plasma temperature $T_e$ and of the photon number density $n_{\gamma }$ characterizing the Universe after the recombination epoch: a system of coupled differential equations for these variables is solved in an analytical way by assuming, as a photon source, PBHs having an initial mass $M\sim {10}^{14}$ g. The results I obtain prove that such a kind of reionization is possible, being able to increase the ionization degree of the Universe from a value x=0.002 (just after the recombination) to values near 1 (when the black holes evaporation ends).