Electromagnetic two-point functions and the Casimir effect in Friedmann-Robertson-Walker cosmologies

TL;DR

This paper analyzes electromagnetic two-point functions in (D+1)-dimensional Friedmann-Robertson-Walker universes, exploring the Casimir effect with conducting plates and how spacetime curvature influences vacuum energy and forces.

Contribution

It provides the first detailed calculation of electromagnetic two-point functions and Casimir forces in curved FRW spacetimes with power-law expansion, including off-diagonal energy flux components.

Findings

Vacuum energy-momentum tensor has nonzero off-diagonal components indicating energy flux.

Casimir forces are attractive at small separations, but can become repulsive at large separations in accelerated universes.

Curvature significantly alters Casimir forces compared to Minkowski spacetime, especially at large distances.

Abstract

We evaluate the two-point functions of the electromagnetic field in (D+1) -dimensional spatially flat Friedmann-Robertson-Walker universes with a power-law scale factor, assuming that the field is prepared in the Bunch-Davies vacuum state. The range of powers are specified in which the two-point functions are infrared convergent and the Bunch-Davies vacuum for the electromagnetic field is a physically realizable state. The two-point functions are applied for the investigation of the vacuum expectation values of the field squared and the energy-momentum tensor, induced by a single and two parallel conducting plates. Unlike to the case of conducting plates in the Minkowski bulk, in the problem under consideration the stresses along the directions parallel to the plates are not equal to the energy density. We show that, in addition to the diagonal components, the vacuum energy-momentum tensor has a nonzero off-diagonal component which describes energy flux along the direction normal to the plates. For a single plate this flux is directed from the plate. The Casimir forces are investigated in the geometry of two plates. At separations between the plates smaller than the curvature radius of the background spacetime, to the leading order, we recover the corresponding result in the Minkowski spacetime and in this case the forces are attractive. At larger separations, the influence of the curvature on the Casimir forces is essential with different asymptotic behavior for decelerated and accelerated expansions. In particular, for the latter case there is a range of powers of the expansion law in which the forces become repulsive at large separations between the plates.