Casimir densities for a plate in de Sitter spacetime

TL;DR

This paper analyzes the vacuum expectation values of a scalar field and the energy-momentum tensor in de Sitter spacetime with a boundary, revealing boundary-induced effects and flux behaviors.

Contribution

It provides explicit formulas for vacuum densities near a boundary in de Sitter space with general curvature coupling and Robin boundary conditions.

Findings

Vacuum energy-momentum tensor is non-diagonal for non-conformal fields.

Boundary induces a flux that can be positive or negative.

Asymptotic behaviors near the boundary and at large distances are characterized.

Abstract

Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with general curvature coupling parameter in the geometry of a plate in the de Sitter spacetime. Robin boundary condition for the field operator is assumed on the plate. The vacuum expectation values are presented as the sum of two terms. The first one corresponds to the geometry of de Sitter bulk without boundaries and the second one is induced by the presence of the plate. We show that for non-conformal fields the vacuum energy-momentum tensor is non-diagonal with the off-diagonal component corresponding to the energy flux along the direction perpendicular to the plate. In dependence of the parameters, this flux can be either positive or negative. The asymptotic behavior of the field squared, vacuum energy density and stresses near the plate and at large distances is investigated.