Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology - art. no. 083003

As the era of high precision cosmology approaches, the empirically determin ed power spectrum of the microwave background anisotropy C, will provide a crucial test for cosmological theories. We present an exact semianalytic fr amework for the study of the sampling statistics of the C, resulting from o bservations with partial sky coverage and anisotropic noise distributions. This includes space-borne, air-borne, and groundbased experiments. We apply this theory to demonstrate its power for constructing fast and unbiased ap proximate methods for the joint estimation of cosmological parameters. Furt her applications, such as a test for possible non-Gaussianity of the underl ying theory and a "poor man's power spectrum estimator" are suggested. An a ppendix derives recursion relations for the efficient computation of the Co uplings between spherical harmonics on the cut sky.