Electromagnetic two-point functions and Casimir densities for a conducting plate in de Sitter spacetime

TL;DR

This paper calculates electromagnetic two-point functions and vacuum expectation values in de Sitter spacetime with a conducting plate, revealing how these quantities depend on the spacetime dimension and distance from the plate.

Contribution

It provides analytical expressions for electromagnetic VEVs in higher-dimensional de Sitter space with boundary conditions, including new insights into their behavior across dimensions.

Findings

Plate-induced electric field squared VEV is positive for 3≤D≤8.

For D≥9, the electric field squared VEV is positive near the plate and negative far away.

The energy-momentum tensor has negative diagonal components and an energy flux directed from the plate.

Abstract

We evaluate the two-point function for the electromagnetic field tensor in $(D+1)$-dimensional de Sitter spacetime assuming that the field is prepared in Bunch-Davies vacuum state. This two-point function is used for the investigation of the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor in the presence of a conducting plate. The VEVs are decomposed into the boundary-free and plate-induced parts. For the latter, closed form analytical expressions are given in terms of the hypergeometric function. For $3\leqslant D\leqslant 8$ the plate-induced part in the VEV of the electric field squared is positive everywhere, whereas for $D\geqslant 9$ it is positive near the plate and negative at large distances. The VEV of the energy-momentum tensor, in addition to the diagonal components, contains an off-diagonal component which corresponds to the energy flux along the direction normal to the plate. Simple asymptotic expressions are provided at small and large distances from the plate compared with the de Sitter curvature scale. For $D\geqslant 4$, all the diagonal components of the plate-induced vacuum energy-momentum tensor are negative and the energy flux is directed from the plate.