Imprints of Cosmic Topology from Early-Universe Quantum Effects

Abstract

Is the Universe infinite in all spatial directions? The answer may lie in the interplay between cosmic topology and quantum effects in the early universe. There are eighteen distinct topologies compatible with spatially flat Friedmann-Lemaître-Robertson-Walker solutions of Einstein’s equations. Seventeen of them--called non-trivial topologies--can be realized by introducing non-trivial topological boundary conditions. These boundary conditions constrain the allowed wavelengths of quantum fields living in such universes; consequently, non-trivial topology induces Casimir effects. We therefore study the backreaction of the Casimir stress-energy tensor of a conformally coupled scalar field in a toroidal universe. Doing so, we quantify the consequences for a pure de Sitter inflationary era and, importantly, we identify signatures that reflect the symmetries broken by the underlying topology.