  In a previous work [S. Rahbardehghan et al. in Phys. Lett. B 750, 627
(2015)], we considered a simple brane-world model; a single $4$-dimensional
brane embedded in a $5$-dimensional de Sitter (dS) space-time. Then, by
including a conformally coupled scalar field in the bulk, we studied the
induced Casimir energy-momentum tensor. Technically, the Krein-Gupta-Bleuler
(KGB) quantization scheme as a covariant and renormalizable quantum field
theory in dS space was used to perform the calculations. In the present paper,
we generalize this study to a less idealized, but physically motivated,
scenario, namely we consider Friedmann-Robertson-Walker (FRW) space-time which
behaves asymptotically as a dS space-time. More precisely, we evaluate Casimir
energy-momentum tensor for a system with two $D$-dimensional curved branes on
background of $D+1$-dimensional FRW space-time with negative spatial curvature
and a conformally coupled bulk scalar field that satisfies Dirichlet boundary
condition on the branes.
