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

TL;DR

This paper develops an analytic framework to compute CMB polarization from adiabatic scalar fluctuations in flat and open universes by extending Hu & Sugiyama’s unpolarized method and applying a tight-coupling expansion. It derives the leading polarization per Fourier mode, provides the multipole expansion for the total polarization, and evaluates the polarization power spectrum and correlation-function multipoles, including Silk damping and the finite width of the last scattering surface. The authors apply the formalism to a COBE-normalized $\Omega_0=1$ CDM model and to open universes, showing that the ratio of temperature to polarization multipoles is highly sensitive to $\Omega_0$ and providing analytic approximations for open and cosmological-constant scenarios. The work highlights how polarization probes the recombination width and ISW effects, offering a tool to constrain cosmological parameters and the ionization history from future CMB polarization data.

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 $Ω_0$, the matter density in units of the critical, in an open universe.