Casimir effect in toroidally compactified de Sitter spacetime

TL;DR

This paper analyzes the Casimir effect in higher-dimensional de Sitter spacetime with compactified dimensions, revealing how topology influences vacuum energy and stresses during different cosmological epochs.

Contribution

It provides a detailed calculation of vacuum expectation values in toroidally compactified de Sitter spacetime, highlighting the topological effects on vacuum energy.

Findings

Topological parts dominate in early universe stages.

Behavior of Casimir densities is independent of curvature coupling for massless fields.

Topological contributions diminish or oscillate at late cosmological times.

Abstract

Vacuum energy density and stresses are investigated for a scalar field with general curvature coupling parameter in (D+1)-dimensional de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The corresponding expectation values are presented in the form of the sum of the vacuum expectation values in uncompactified dS spacetime and the part induced by the non-trivial topology. In the early stages of the cosmological evolution the topological parts dominate. In this limit the behavior of the Casimir densities does not depend on the curvature coupling parameter and coincides with that for a conformally coupled massless field. At late stages of the cosmological expansion the expectation values are dominated by the part corresponding to uncompactified dS spacetime. The vanishing of the topological parts is monotonic or oscillatory in dependence of the mass and the curvature coupling parameter of the field.