Polarization of the Cosmic Microwave Background in a Reionized Universe

In this work I study the polarization of the Cosmic Microwave Background (CMB) induced by a cosmological background of gravitational waves (here GWs) and I discuss the enhancement effect of a possible late and fast reionization of the Universe, caused by the Hawking evaporation of primordial black holes and happening at a redshift $z\sim 20\div 30$. Then, I solve the radiative Boltzmann transfer equation in the form of a second-kind Volterra integral equation, by using the analytical method of the iterated kernels: this particular method can be successfully applied when we have an exponential kernel, as in the case when the Universe is reionized by the intense particle emission coming from evaporating primordial black holes.