Temperature Correlations in a Finite Universe

Abstract

We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all possible finite flat models. We examine the angular correlation function itself, pointing out visible and discrete features that arise from topology. While observations of the power spectrum on large angular scales can be used to place bounds on the minimum topology length, cosmic variance generally restricts us from differentiating one flat topology from another. Schemes that acknowledge anisotropic structures, such as searches for ghosts, circles or geometric patterns, will be needed to further probe topology.