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.

Revised version with corrections to eqs.(2.18-20), slight changes in Figs. 1 and 2, and additional comments at the end of Sect. IV. RevTex, 20 pages + 4 Postcript figures in separate file

References in corpus (10)

• Anisotropies in the Cosmic Microwave Background: An Analytic Approach
• Toward Understanding CMB Anisotropies and Their Implications
• Polarization of the Microwave Background due to Primordial Gravitational Waves
• Measuring Cosmological Parameters with Cosmic Microwave Background Experiments
• A Two-Fluid Approximation for Calculating the Cosmic Microwave Background Anisotropies
• Polarization and Anisotropy of the Microwave Sky
• Large-Angle Cosmic Microwave Background Anisotropies in an Open Universe
• Polarization of the Microwave Background in Inflationary Cosmology
• Gravitational Waves and the Polarisation of the Cosmic Microwave Background
• Large-scale Polarization of the Cosmic Microwave Background Radiation

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