  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.
