Casimir effect in spacetime with extra dimensions - from Kaluza-Klein to Randall-Sundrum models

In this Letter, 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.