The standard cosmological model does not determine the spatial topology of the Universe. This article revisits the signature of a nontrivial topology on the properties of the cosmic microwave background anisotropies. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature that can be used to distinguish a multiconnected space from an infinite space on sizes larger than the last scattering surface. The effect of the instrumental noise and of a Galactic cut are estimated. We thus establish boundaries for the size of the biggest torus distinguishable with temperature and polarization CMB data. We also describe the imprint of the spatial topology on the 3-point function and on non-Gaussianity.

• Received 28 January 2014

DOI:https://doi.org/10.1103/PhysRevD.92.043003