Bulk photons in Asymmetrically Warped Space-times and Non-trivial Vacuum Refractive Index

TL;DR

This paper investigates how asymmetrically warped brane models with bulk photons lead to an energy-dependent speed of light, resulting in a non-trivial vacuum refractive index, and compares predictions with astrophysical observations to constrain model parameters.

Contribution

It demonstrates that bulk photons in asymmetrically warped brane models exhibit a nonlinear dispersion relation, causing an energy-dependent refractive index, and applies observational data to restrict these models.

Findings

Photon speed becomes energy-dependent due to nonlinear dispersion.

The effective refractive index is sub-luminous and proportional to photon energy squared.

Astrophysical data from MAGIC Telescope constrains model parameters.

Abstract

We consider asymmetrically warped brane models, or equivalently brane models where the background metric is characterized by different time and space warp factors. The main feature of these models is that 4D Lorentz symmetry is violated for fields which propagate in the bulk, such as gravitons. In this paper we examine the case of bulk photons in asymmetrically warped brane models. Although our results are general, we examine here two specific but characteristic solutions: 1) AdS-Schwarzschild 5D Black Hole solution and 2) AdS-Reissner Nordstrom 5D Black Hole solution. We show that the standard Lorentz invariant dispersion relation for 4D photons is corrected by nonlinear terms which lead to an Energy-dependent speed of light. Specifically, we obtain a sub-luminous Energy-dependent refractive index of the form n_{eff}(\omega)=1+c_{G} \omega^2, where \omega is the energy of the photon, and the factor c_G is always positive and depends on the free parameters of the model. Finally, comparing the results with recent data from the MAGIC Telescope, claiming a delayed arrival of photons from the Active Galactic Nucleus of Mk501, we impose concrete restrictions to the two sets of models examined in this work. We shall also discuss briefly other possible astrophysical constraints on our models.