Casimir effect in de Sitter spacetime

TL;DR

This paper investigates the Casimir effect for a scalar field in de Sitter spacetime, revealing how spacetime curvature influences vacuum energy and forces between plates, with different regimes depending on field parameters.

Contribution

It provides a detailed analysis of the vacuum energy-momentum tensor and Casimir forces in de Sitter space, including the effects of curvature, mass, and boundary conditions, which was not previously explored.

Findings

Casimir forces are affected by spacetime curvature at large separations.

Two regimes of force behavior: monotonic and oscillatory, depending on parameters.

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

Abstract

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two 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. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.