Casimir densities for a spherical boundary in de Sitter spacetime

TL;DR

This paper investigates quantum vacuum effects for a scalar field with boundary conditions in de Sitter space, revealing how boundaries influence energy-momentum and flux, with results depending on field mass and coupling.

Contribution

It provides explicit calculations of vacuum expectation values for a scalar field with Robin boundary conditions in de Sitter space, including boundary and non-boundary contributions.

Findings

Vacuum energy-momentum tensor is non-diagonal with radial energy flux.

Boundary-induced expectation values decay as a power-law at large distances.

Behavior of expectation values varies between monotonic and oscillatory depending on field parameters.

Abstract

Two-point functions, mean-squared fluctuations, and the vacuum expectation value of the energy-momentum tensor operator are investigated for a massive scalar field with an arbitrary curvature coupling parameter, subject to a spherical boundary in 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 sphere. Both the interior and exterior regions are considered. For the calculation in the interior region, a mode-summation method is employed, supplemented with a variant of the generalized Abel-Plana formula. This allows us to explicitly extract the contributions to the expectation values which come from de Sitter spacetime without boundaries. We show that the vacuum energy-momentum tensor is non-diagonal with the off-diagonal component corresponding to the energy flux along the radial direction. With dependence on the boundary condition and the mass of the field, this flux can be either positive or negative. Several limiting cases of interest are then studied. 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, far from the sphere. The decay of the boundary induced expectation values at large distances from the sphere is shown to be power-law (monotonic or oscillating), independent of the value of the field mass.