Theory of Cosmic Microwave Background Polarization

Details Theory of Cosmic Microwave Background Polarization Theory of Cosmic Microwave Background Polarization

2004-03-16

arxiv.org/abs/astro-ph/0403392v2

Astronomy and Astrophysics

Astrophysics

32 pages, 8 figures. Lectures given at the 2003 Villa Mondragone School of Gravitation and Cosmology: ``The Polarization of th

Scientific paper

These lectures introduce some of the basic theory of cosmic microwave background (CMB) polarization with the primary aim of developing the theory of CMB polarization from inflationary gravitational waves, as well as some of the related theory of weak gravitational lensing (cosmic shear) of CMB polarization. We begin with production of polarization by Thomson scattering. We then discuss tensor-harmonic analysis (the ``grad-curl'' or ``E-B'' decomposition) on a flat and full sky in some detail. The Boltzmann/Einstein equations required to predict the CMB temperature/polarization pattern due to primordial gravitational waves are derived. We show that gravitational waves produce a curl component of the CMB polarization while density perturbations (at linear order) do not. We then show how cosmic shear induces a curl component from a curl-free surface of last scattering. We describe, though in less detail, how higher-order correlations can be used to subtract the cosmic-shear--induced curl. Several exercises are provided.

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