Statistics of cosmic microwave background polarization
Abstract
We present a formalism for analyzing a fullsky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the twopoint correlation function. Polarization, which is described by a secondrank tensor, can be treated analogously by expanding in the appropriate tensor spherical harmonics. We provide expressions for the complete set of temperature and polarization multipole moments for scalar and tensor metric perturbations. Four sets of multipole moments completely describe isotropic temperature and polarization correlations; for scalar metric perturbations one set is identically zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole moments can be measured in idealized experiments is evaluated, including the effects of detector noise, sky coverage, and beam width. Finally, we construct coordinateindependent polarization twopoint correlation functions, express them in terms of the multipole moments, and derive smallangle limits.
 Publication:

Physical Review D
 Pub Date:
 June 1997
 DOI:
 10.1103/PhysRevD.55.7368
 arXiv:
 arXiv:astroph/9611125
 Bibcode:
 1997PhRvD..55.7368K
 Keywords:

 98.70.Vc;
 98.80.Cq;
 Background radiations;
 Particletheory and fieldtheory models of the early Universe;
 Astrophysics;
 High Energy Physics  Phenomenology
 EPrint:
 28 pages, RevTeX