The influence of a spherical boundary on the vacuum fluctuations of a massive scalar field is investigated in background of (D + 1)-dimensional Milne universe, assuming that the field obeys Robin boundary condition on the sphere. The normalized mode functions are derived for the regions inside and outside the sphere and different vacuum states are discussed. For the conformal vacuum, the Hadamard function is decomposed into boundary-free and sphere-induced contributions and an integral representation is obtained for the latter in both the interior and exterior regions. As important local characteristics of the vacuum state the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor are investigated. It is shown that the vacuum energy-momentum tensor has an off-diagonal component that corresponds to the energy flux along the radial direction. Depending on the coefficient in Robin boundary condition the sphere-induced contribution to the vacuum energy and the energy flux can be either positive or negative. At late stages of the expansion and for a massive field the decay of the sphere-induced VEVs, as functions of time, is damping oscillatory. The geometry under consideration is conformally related to that for a static spacetime with negative constant curvature space and the sphere-induced contributions in the corresponding VEVs are compared.
We investigate quantum vacuum effects for a massive scalar field, induced by two planar boundaries in background of a linearly expanding spatially flat Friedmann-Robertson-Walker spacetime for an arbitrary number of spatial dimensions. For the Robin boundary conditions and for general curvature coupling parameter, a complete set of mode functions is presented and the related Hadamard function is evaluated. The results are specified for the most important special cases of the adiabatic and conformal vacuum states. The vacuum expectation values of the field squared and of the energy-momentum tensor are investigated for a massive conformally coupled field. The vacuum energy-momentum tensor, in addition to the diagonal components, has nonzero off-diagonal component describing energy flux along the direction perpendicular to the plates. The influence of the gravitational field on the local characteristics of the vacuum state is essential at distances from the boundaries larger than the curvature radius of the background spacetime. In contrast to the Minkowskian bulk, at large distances the boundary-induced expectation values follow as power law for both massless and massive fields. Another difference is that the Casimir forces acting on the separate plates do not coincide if the corresponding Robin coefficients are different. At large separations between the plates the decay of the forces is power law. We show that during the cosmological expansion the forces may change the sign.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.