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

TL;DR

This paper extends previous work on Casimir energy-momentum tensors for a scalar field in de Sitter space to a more realistic Friedmann-Robertson-Walker background with two curved branes, analyzing quantum effects in a cosmological setting.

Contribution

It generalizes the calculation of Casimir energy-momentum tensors from de Sitter space to FRW space-time with curved branes, using conformally coupled scalar fields and Dirichlet boundary conditions.

Findings

Casimir energy-momentum tensor evaluated for two curved branes in FRW background.

Results show dependence of quantum vacuum effects on brane curvature and separation.

Provides insights into quantum field behavior in cosmological brane-world models.

Abstract

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.