Casimir force for a scalar field in warped brane worlds

Abstract

In looking for imprints of extra dimensions in brane world models one usually builts these so that they are compatible with known low energy physics and thus focuses on high energy effects. Nevertheless, just as submillimeter Newton's law tests probe the mode structure of gravity other low energy tests might apply to matter. As a model example, in this work we determine the 4D Casimir force corresponding to a scalar field subject to Dirichlet boundary conditions on two parallel planes lying within the single brane of a Randall-Sundrum scenario extended by one compact extra dimension. Using the Green's function method such a force picks the contribution of each field mode as if it acted individually but with a weight given by the square of the mode wave functions on the brane. In the low energy regime one regains the standard 4D Casimir force that is associated to a zero mode in the massless case or to a quasilocalized or resonant mode in the massive one whilst the effect of the extra dimensions gets encoded as an additional term.

22 pages, 2 figures

References in corpus (5)

• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• The Casimir Force in Randall Sundrum Models
• On the Casimir effect for parallel plates in the spacetime with one extra compactified dimension
• Using Muonic Hydrogen in Optical Spectroscopy Experiment to Detect Extra Dimensions
• Low-energy effects in brane worlds: Liennard-Wiechert potentials and Hydrogen Lamb shift

Cited by in corpus (20)

• The Casimir Force in Randall Sundrum Models with q+1 dimensions
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Finite temperature Casimir effect in spacetime with extra compactified dimensions
• Induced vacuum currents in anti-de Sitter space with toral dimensions
• Fermionic current from topology and boundaries with applications to higher-dimensional models and nanophysics
• Casimir force in brane worlds: coinciding results from Green's and Zeta function approaches
• Finite Temperature Casimir Effect for Massless Majorana Fermions in a Magnetic Field
• Fermionic currents in AdS spacetime with compact dimensions
• The Casimir effect for parallel plates involving massless Majorana fermions at finite temperature
• A de Sitter tachyonic braneworld revisited
• Brane world corrections to scalar vacuum force in RSII-p
• Cosmic string and brane induced effects on the fermionic vacuum in AdS spacetime
• Casimir effect for curved boundaries in Robertson-Walker spacetime
• Wightman function and the Casimir effect for a Robin sphere in a constant curvature space
• Electromagnetic Casimir piston in higher dimensional spacetimes
• Vacuum densities and the Casimir forces for branes orthogonal to the AdS boundary
• Casimir force for cosmological domain walls
• Casimir densities in brane models with compact internal spaces
• Electromagnetic Wightman functions and vacuum densities for a brane intersecting the AdS boundary