Finite Temperature Casimir Effect in Randall-Sundrum Models

TL;DR

This paper investigates the finite temperature Casimir effect in Randall-Sundrum models, calculating energy and force for scalar fields with various boundary conditions, and discusses temperature effects at different regimes.

Contribution

It provides a detailed analysis of the finite temperature Casimir effect in RSI and RSII models, including explicit calculations and boundary condition considerations.

Findings

Temperature correction can be attractive or repulsive depending on conditions.

Explicit formulas for Casimir energy and force at different temperatures.

Use of Abel-Plana formula simplifies the summation process.

Abstract

The finite temperature Casimir effect for a scalar field in the bulk region of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation $a$ on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attractiveness versus repulsiveness of the temperature correction to the force is discussed in the typical special cases of Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is made use of, as this turns out to be most convenient. Some comments are made on the related contemporary literature.