Vacuum quantum effect for curved boundaries in static Robertson-Walker space-time

The energy-momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k=−1 static Robertson-Walker space-time 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.