ALL-SKY ANALYSIS OF POLARIZATION IN THE MICROWAVE BACKGROUND

Using the formalism of spin-weighted functions we present an all-sky a nalysis of polarization in the cosmic microwave background (CMB). Line ar polarization is a second-rank symmetric and traceless tensor, which can be decomposed on a sphere into spin +/-2 spherical harmonics. The se are the analogues of the spherical harmonics used in the temperatur e maps and obey the same completeness and orthogonality relations. We show that there exist two linear combinations of spin +/-2 multipole m oments which have opposite parities and can be used to fully character ize the statistical properties of polarization in the CMB. Magnetic-ty pe parity combination does not receive contributions from scalar modes and does not cross correlate with either temperature or electric-type parity combination, so there are four different power spectra that fu lly characterize statistical properties of CMB. We present their expli cit expressions for scalar and tensor modes in the form of line of sig ht integral solution and numerically evaluate them for a representativ e set of models. These general solutions differ from the expressions o btained previously in the small scale limit both for scalar and tensor modes. A method to generate and analyze all-sky maps of temperature a nd polarization is given and the optimal estimators for various power spectra and their corresponding variances are discussed.