Topology beyond the horizon: how far can it be probed?

Abstract

The standard cosmological model does not determine the spatial topology of the universe. This article revisits the signature of a non-trivial 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 multi-connected 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 dintinguisable with temperature and polarization CMB data. We also describe the imprint of the spatial topology on the 3-point function and on non-Gaussianity.

20 pages, 24 figures

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• Promise of Future Searches for Cosmic Topology
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• Tensor perturbations during inflation in a spatially closed Universe
• Weak-lensing $B$-modes as a probe of the isotropy of the universe
• The variance of the CMB temperature gradient: a new signature of a multiply connected Universe
• Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
• Cosmic topology. Part IIIa. Microwave background parity violation without parity-violating microphysics
• Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes
• Gravitational Interaction in the Chimney Lattice Universe
• Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds
• Gravitational potentials and forces in the Lattice Universe: a slab
• The emergent Big Bang scenario