Casimir Effect for Moving Branes in Static dS$_{4+1}$ Bulk

TL;DR

This paper investigates the Casimir effect for conformally coupled scalar fields in a static de Sitter background with moving branes, deriving vacuum energy-momentum tensors via conformal transformations from Rindler space.

Contribution

It provides a novel calculation of the vacuum energy-momentum tensor for moving branes in static de Sitter space using conformal relations to Rindler space.

Findings

Vacuum expectation values obtained via conformal transformation.

Analysis of boundary conditions on moving branes.

Explicit expressions for energy-momentum tensor in the given setup.

Abstract

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS$_{4+1}$ spacetime. We will consider the general plane--symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.