Shape of a small universe: Signatures in the cosmic microwave background

We consider the most general parametrization of flat topologically compact universes, complementing the work of Scannapieco, Levin and Silk to include nontrivial shapes. We find that modifications in the 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.