Large-scale anisotropy of the cosmic background radiation in Friedmann universes

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Abstract
We compute the large-scale anisotropy of the cosmic background radiation due to the gravitational field of clumped matter in open, closed, and flat Friedmann universes. Formulas are derived for the mean-square angular fluctuation of the cosmic background radiation in terms of the two-point correlation function of matter. The results depend importantly on whether or not the matter perturbations locally satisfy the integral constraints which express local conservation of energy and momentum, and we discuss these two possibilities. We examine the behavior as spatial curvature goes to zero.