The accurate understanding of the ionization history of the Universe plays a fundamental role in modern cosmology. It includes a phase of cosmological reionization after the standard recombination epoch, possibly associated to the early stages of structure and star formation. While the simple “τ-parametrization” of the reionization process and, in particular, of its imprints on the Cosmic Microwave Background (CMB) anisotropy likely represents a sufficiently accurate modelling for the interpretation of current CMB data, a great attention has been recently posed on the accurate computation of the reionization signatures in the CMB for a large variety of astrophysical scenarios and physical processes. The amplitude and shape of the B-mode Angular Power Spectrum (APS) depends, in particular, on the tensortoscalar ratio, r, related to the energy scale of inflation, and on the reionization history, thus an accurate modeling of the reionization process will have implications for the precise determination of r or to set more precise constraints on it through the joint analysis of E and B-mode polarization data available in the next future and from a mission of next generation. In this work we review some classes of astrophysical and phenomenological reionization histories, beyond the simpleτ-parametrization, a present a careful characterization of the imprints introduced in all the CMB APS modes. We have implemented a modified version of CAMB, the Cosmological Boltzmann code for computing the CMB anisotropy APS, to introduce the predicted hydrogen and helium ionization fractions. We compared the results obtained for these models for all the non-vanishing (in the assumed scenarios) modes of the CMB APS. Considering also the limitation from potential residuals of astrophysical foregrounds, we discussed the capability of next data to disentangle between different reionization scenarios in a wide range of tensor-to-scalar ratios.
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