Casimir effect in de Sitter and Anti-de Sitter braneworlds

TL;DR

This paper investigates the Casimir effect in five-dimensional de Sitter and Anti-de Sitter braneworlds, showing quantum effects can stabilize branes and influence cosmological constants.

Contribution

It provides a detailed analysis of the bulk Casimir effect in braneworld models, demonstrating stabilization mechanisms and quantum corrections to the radion potential.

Findings

Casimir effect can stabilize dS and AdS braneworlds.

Quantum corrections deform the de Sitter brane.

Bulk quantum effects may reduce the four-dimensional cosmological constant.

Abstract

We discuss the bulk Casimir effect (effective potential) for a conformal or massive scalar when the bulk represents five-dimensional AdS or dS space with two or one four-dimensional dS brane, which may correspond to our universe. Using zeta-regularization, the interesting conclusion is reached, that for both bulks in the one-brane limit the effective potential corresponding to the massive or to the conformal scalar is zero. The radion potential in the presence of quantum corrections is found. It is demonstrated that both the dS and the AdS braneworlds may be stabilized by using the Casimir force only. A brief study indicates that bulk quantum effects are relevant for brane cosmology, because they do deform the de Sitter brane. They may also provide a natural mechanism yielding a decrease of the four-dimensional cosmological constant on the physical brane of the two-brane configuration.