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Casimir energy-momentum tensor for a quantized bulk scalar field in the geometry of two curved branes on Friedmann-Robertson-Walker background

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.