Topological Casimir effect in power-law FRW cosmologies

TL;DR

This paper studies the quantum vacuum effects in expanding cosmological models with compactified dimensions, revealing how topology and curvature coupling influence vacuum energy and field fluctuations.

Contribution

It provides a comprehensive analysis of the topological Casimir effect in power-law FRW universes with arbitrary compactification and curvature coupling.

Findings

Vacuum expectation values depend on the size of compact dimensions and curvature coupling.

Short compact dimensions yield conformal coupling results, matching adiabatic approximation.

Large compact dimensions exhibit monotonic or oscillatory behavior based on curvature coupling.

Abstract

We investigate the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. When the comoving lengths of the compact dimensions are short compared to the Hubble length, the topological parts coincide with those for a conformal coupling. This limit corresponds to the adiabatic approximation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the curvature coupling parameter, two regimes are realized with monotonic or oscillatory behavior of the vacuum expectation values.