Casimir energy for de Sitter branes in bulk AdS(5)

TL;DR

This paper calculates the vacuum energy (Casimir energy) for a scalar field in a de Sitter brane setup within AdS(5), revealing zero energy for one brane and non-zero for two branes, with implications for brane-world models.

Contribution

It provides a detailed calculation of Casimir energy in a de Sitter brane in AdS(5), including effects of conformal coupling and brane configurations, using zeta-function regularisation.

Findings

Vacuum energy is zero for a single brane.

Vacuum energy is non-zero for two branes.

Comments on back-reaction and non-conformal couplings.

Abstract

The vacuum energy for a massless conformally coupled scalar field in a brane world set up, corresponding to de Sitter branes in a bulk anti-de Sitter spacetime, is calculated. We use the Euclidean version of the metric which can be conformally related to a metric similar in form to the Einstein universe (S^4 times R). Employing zeta-function regularisation we evaluate the one-loop effective potential and show that the vacuum energy is zero for the one brane and non-zero for the two brane configuration. We comment on the back-reaction of this Casimir energy and on the inclusion of a mass term or non-conformal coupling.