The shape of a small universe: signatures in the cosmic microwave background

Abstract

We consider the most general parametrization of flat topologically compact universes, complementing the work of Scannapieco, Levin and Silk to include non-trivial shapes. We find that modifications in shape of the fundamental domain will lead to distinct signatures in the anisotropy of the cosmic microwave radiation. We make a preliminary assessment of the effect on three statistics: the angular power spectrum, the distribution of identified ``circles'' on the surface of last scattering and the correlation function of antipodal points.

5 pages, 3 figures, accepted for publication in Phys. Rev. D