STATISTICS OF COSMIC MICROWAVE BACKGROUND POLARIZATION

We present a formalism for analyzing a full-sky temperature and polari zation map of the cosmic microwave background. Temperature maps are an alyzed by expanding over the set of spherical harmonics to give multip ole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by e xpanding in the appropriate tensor spherical harmonics. We provide exp ressions for the complete set of temperature and polarization multipol e moments for scalar and tensor metric perturbations. Four sets of mul tipole moments completely describe isotropic temperature and polarizat ion correlations; for scalar metric perturbations one set is identical ly zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole momen ts can be measured in idealized experiments is evaluated, including th e effects of detector noise, sky coverage, and beam width. Finally, we construct coordinate-independent polarization two-point correlation f unctions, express them in terms of the multipole moments, and derive s mall-angle limits.