Vacuum quantum effect for curved boundaries in static Robertson--Walker spacetime

The energy-momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in $k=-1$ static Robertson–Walker spacetime is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. $k=-1$ Robertson–Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in Robertson–Walker space from the corresponding Rindler counterpart by the conformal transformation.