Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves

We present an approximate, analytical calculation of the reionized spectra C l of cosmic microwave background radiation (CMB) anisotropies and polarizations generated by relic gravitational waves (RGWs). Three simple models of reionization are explored, whose visibility functions are fitted by gaussian type of functions as approximations. We have derived the analytical polarization βl and temperature anisotropies αl, both consisting of two terms proportional to RGWs at the decoupling and at the reionization as well. The explicit dependence of βl and αl upon the reionization time ηr, the duration ∆ηr, and the optical depth κr are demonstrated. Moreover, βl and αl contain κr in different coefficients, and the polarization spectra C l are C l are more sensitive probes of reionization than C l . These results facilitate examination of the reionization effects, in particular, the degeneracies of κr with the normalization amplitude and with the initial spectral index of RGWs. ∗[email protected]