The Casimir force on a piston in Randall-Sundrum models

TL;DR

This paper investigates the Casimir force on a piston within Randall-Sundrum models, deriving expressions and analyzing force behavior, revealing attraction at close distances and repulsion at larger separations, with implications for experimental observations.

Contribution

It provides the first detailed calculation of Casimir forces on a piston in Randall-Sundrum models, including force behavior and limits, extending understanding of quantum effects in higher-dimensional theories.

Findings

Attractive force when plates are very close in two-brane models

Force becomes repulsive at larger separations in two-brane models

Force shape similar to four-dimensional case in one-brane models

Abstract

The Casimir effect of a piston for massless scalar fields which satisfy Dirichlet boundary conditions in the context of five-dimensional Randall-Sundrum models is studied. In these scenarios we derive and calculate the expression for the Casimir force on the piston. We also discuss the Casimir force in the limit that one outer plate is moved to the remote place to show that the nature of the reduced force between the parallel plates left. In the Randall-Sundrum model involving two branes the two plates attract each other when they locate very close, but the reduced Casimir force turns to be repulsive as the plates separation is not extremely tiny, which is against the experimental phenomena. In the case of one brane model the shape of the reduced Casimir force is similar to that of the standard two-parallel-system in the four-dimensional flat spacetimes while the sign of force remains negative.