Casimir effect in de Sitter spacetime with compactified dimension

TL;DR

This paper analyzes the quantum vacuum effects of a scalar field in de Sitter spacetime with one compactified dimension, revealing how topology influences vacuum energy and stress, especially during early cosmological times.

Contribution

It provides explicit calculations of vacuum expectation values in de Sitter space with compactification, highlighting the topological effects on vacuum energy and their evolution over time.

Findings

Topological part violates local de Sitter symmetry.

Topological vacuum stresses dominate early universe.

At late times, stresses become isotropic and resemble an effective gravitational source.

Abstract

We investigate the Hadamard function, the vacuum expectation values of the field square and the energy-momentum tensor of a scalar field with general curvature coupling parameter in de Sitter spacetime compactified along one of spatial dimensions. By using the Abel-Plana summation formula, we have explicitly extracted from the vacuum expectation values the part due to the compactness of the spatial dimension. The topological part in the vacuum energy-momentum tensor violates the local de Sitter symmetry and dominates in the early stages of the cosmological evolution. At late times the corresponding vacuum stresses are isotropic and the topological part corresponds to an effective gravitational source with barotropic equation of state.