Analytic approach to the polarization of the cosmic microwave background in flat and open universes

Abstract

We develop an analytic method and approximations to compute the polarization induced in the cosmic microwave background radiation on a wide range of angular scales by anisotropic Thomson scattering in presence of adiabatic scalar {(energy-density)} linear fluctuations. The formalism is an extension to the polarized case of the analytic approach recently developed by Hu and Sugiyama to evaluate the (unpolarized) temperature correlation function. The analytic approach helps to highlight the dependence of potentially measurable polarization properties of the cosmic microwave background radiation upon various parameters of the cosmological model. We show, for instance, that the ratio between the multipoles of the temperature and polarization correlation functions depends very sensitively upon the value of $\Omega_0$, the matter density in units of the critical, in an open universe.