Finite-temperature Casimir effect in Randall-Sundrum models

Abstract

The finite-temperature Casimir effect for a scalar field in the bulk region of 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. Hightemperature and low-temperature cases are covered. Attraction versus repulsion of the temperature correction to the force is discussed in the special cases of Dirichlet–Dirichlet, Neumann–Neumann and Dirichlet–Neumann boundary conditions at low temperature. The Abel–Plana summation formula is used, as this is found to be the most convenient. Some comments are made on the related contemporary literature.