Electromagnetic Casimir densities for a cylindrical shell on de Sitter space

TL;DR

This paper calculates electromagnetic vacuum densities around a cylindrical shell in de Sitter space, revealing how curvature and boundary conditions influence quantum field behavior and Casimir forces.

Contribution

It provides explicit formulas for electromagnetic vacuum expectation values in cylindrical geometries within de Sitter space, including boundary effects and extensions to Minkowski space.

Findings

Shell-induced electric field squared is positive inside and outside.

Casimir-Polder forces are directed toward the shell.

Vacuum energy flux flows outward from the shell.

Abstract

Complete set of cylindrical modes is constructed for the electromagnetic field inside and outside a cylindrical shell in the background of $(D+1)$% -dimensional dS spacetime. On the shell, the field obeys the generalized perfect conductor boundary condition. For the Bunch-Davies vacuum state, we evaluate the expectation values (VEVs) of the electric field squared and of the energy-momentum tensor. The shell-induced contributions are explicitly extracted. In this way, for points away from the shell, the renormalization is reduced to the one for the VEVs in the boundary-free dS bulk. As a special case, the VEVs are obtained for a cylindrical shell in the $(D+1)$% -dimensional Minkowski bulk. We show that the shell-induced contribution in the electric field squared is positive for both the interior and exterior regions. The corresponding Casimir-Polder forces are directed toward the shell. The vacuum energy-momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component corresponding to the energy flux along the direction normal to the shell. This flux is directed from the shell in both the exterior and interior regions. For points near the shell, the leading terms in the asymptotic expansions for the electric field squared and diagonal components of the energy-momentum tensor are obtained from the corresponding expressions in the Minkowski bulk replacing the distance from the shell by the proper distance in the dS bulk. The influence of the gravitational field on the local characteristics of the vacuum is essential at distances from the shell larger than the dS curvature radius. The results are extended for confining boundary conditions of flux tube models in QCD.