Electromagnetic Casimir effect for conducting plates in de Sitter spacetime

TL;DR

This paper investigates the electromagnetic Casimir effect between parallel plates in de Sitter spacetime, revealing how the gravitational background alters the vacuum energy and force behavior compared to flat spacetime, especially for higher dimensions.

Contribution

It provides a detailed analysis of the electromagnetic vacuum expectation values and Casimir forces in de Sitter spacetime with generalized boundary conditions across multiple dimensions.

Findings

Casimir forces decay as inverse fourth power of distance at large separations.

Gravitational field significantly alters vacuum energy behavior for D≥4.

Force decay differs from Minkowski spacetime, especially for D≥4.

Abstract

Two-point functions, the mean field squared and the vacuum expectation value (VEV) of the energy-momentum tensor are investigated for the electromagnetic field in the geometry of parallel plates on background of $(D+1)$% -dimensional dS spacetime. We assume that the field is prepared in the Bunch-Davies vacuum state and on the plates a boundary condition is imposed that is a generalization of the perfectly conducting boundary condition for an arbitrary number of spatial dimensions. It is shown that for $D\geq 4$ the background gravitational field essentially changes the behavior of the VEVs at separations between the plates larger than the curvature radius of dS spacetime. At large separations, the Casimir forces are proportional to the inverse fourth power of the distance for all values of spatial dimension $D\geq 3$. For $D\geq 4$ this behavior is in sharp contrast with the case of plates in Minkowski bulk where the force decays as the inverse $(D+1)$th power of the distance.