Casimir effect for parallel plates in de Sitter spacetime

TL;DR

This paper investigates the Casimir effect for a scalar field between parallel plates in de Sitter spacetime, analyzing vacuum expectation values, boundary conditions, and the influence of spacetime curvature on Casimir forces.

Contribution

It provides explicit calculations of vacuum expectation values and Casimir forces in de Sitter space with Robin boundary conditions, highlighting the curvature's impact on force behavior.

Findings

Curvature significantly affects Casimir force behavior at large separations.

Vacuum expectation values exhibit monotonic or oscillatory regimes depending on parameters.

Casimir force decay follows a power-law, independent of field mass.

Abstract

The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows to explicitly extract the contributions to the expectation values which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power-law (monotonic or oscillating), with independence of the value of the field mass.