Casimir Effect in Spacetime with Extra Dimensions -- From Kaluza-Klein to Randall-Sundrum Models

TL;DR

This paper derives exact finite temperature Casimir force formulas for a massless scalar field in higher-dimensional brane models, showing that warped extra dimensions do not alter the force's sign, contrary to previous speculations.

Contribution

It provides exact formulas for the Casimir force in higher-dimensional models, correcting prior approximations and clarifying the effect of warped extra dimensions.

Findings

Exact formulas for Casimir force at finite temperature

Warped extra dimensions do not change the force's sign

Disproves previous speculation about force sign change

Abstract

In this article, we derive the finite temperature Casimir force acting on a pair of parallel plates due to a massless scalar field propagating in the bulk of a higher dimensional brane model. In contrast to previous works which used approximations for the effective masses in deriving the Casimir force, the formulas of the Casimir force we derive are exact formulas. Our results disprove the speculations that existence of the warped extra dimension can change the sign of the Casimir force, be it at zero or any finite temperature.