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Published June 15, 1997 | Published
Journal Article Open

Statistics of cosmic microwave background polarization


We present a formalism for analyzing a full-sky 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 two-point correlation function. Polarization, which is described by a second-rank 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 coordinate-independent polarization two-point correlation functions, express them in terms of the multipole moments, and derive small-angle limits.

Additional Information

© 1997 The American Physical Society Received 18 November 1996 We would like to thank Jerry Jungman, Lloyd Knox, and Uros Seljak for helpful conversations, and David Spergel and Gary Hinshaw for stimulating questions. This work was supported by U.S. DOE Contract No. DEFG02-92-ER 40699, NASA NAG5-3091, and the Alfred P. Sloan Foundation at Columbia, NASA AST94-19400 at Fermilab, and the Harvard Society of Fellows. M.K. acknowledges the hospitality of the NASA/Fermilab Astrophysics Center and the CERN Theory Group.

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