Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Abstract

We evaluate the positive-frequency Wightman function, the vacuum expectation values (VEVs) of the field squared, and the energy–momentum tensor for a massive scalar field with general curvature coupling for a cylindrical shell in the background of de Sitter (dS) spacetime. The field is prepared in the Bunch–Davies vacuum state and on the shell, and the corresponding operator obeys the Robin boundary condition (BC). In the region inside the shell and for non-Neumann BC, the Bunch–Davies vacuum is a physically realizable state for all values of the mass and curvature coupling parameter. For both interior and exterior regions, the VEVs are decomposed into boundary-free dS and shell-induced parts. We show that the shell-induced part of the vacuum energy–momentum tensor has a nonzero off-diagonal component corresponding to the energy flux along the radial direction. Unlike in the case of a shell in Minkowski bulk, for the dS background, the axial stresses are not equal to the energy density. In dependence of the mass and the coefficient in the BC, the vacuum energy density and the energy flux can be either positive or negative. The influence of the background gravitational field on the boundary-induced effects is crucial at distances from the shell larger than the dS curvature scale. In particular, the decay of the VEVs with distance is power-law (monotonic or oscillatory with dependence of the mass) for both massless and massive fields. For the Neumann BC, the decay is faster than that for non-Neumann conditions.