Theory of Cosmic Microwave Background Polarization
Abstract
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 tensorharmonic analysis (the ``gradcurl'' or ``EB'' 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 curlfree surface of last scattering. We describe, though in less detail, how higherorder correlations can be used to subtract the cosmicshearinduced curl. Several exercises are provided.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:astroph/0403392
 Bibcode:
 2004astro.ph..3392C
 Keywords:

 Astrophysics
 EPrint:
 32 pages, 8 figures. Lectures given at the 2003 Villa Mondragone School of Gravitation and Cosmology: ``The Polarization of the Cosmic Microwave Background,'' Rome, Italy, September 611, 2003. Revised version (March '05) fixes several typographical errors