Branes on Charged Dilatonic Backgrounds: Self-Tuning, Lorentz Violations and Cosmology

TL;DR

This work investigates brane-world cosmology in a charged dilatonic bulk by constructing a general $d=n+q+2$ background with a dilaton and a $(q+2)$-form, where $n$-dimensional slices have constant curvature $k\in\{0,+1,-1\}$. It embeds a codimension-one brane ($q=0$) and derives the Israel junction conditions, yielding a Friedmann-like equation that ties the brane's dynamics to the bulk geometry and the dilaton/gauge couplings, with the brane’s equation of state $\omega$ constrained by these couplings. Specializing to $d=5$ (i.e., $n=3$) the paper recovers and extends known scalar and gauge-field self-tuning scenarios, showing that including gauge fields can shield bulk singularities and permit physically reasonable $\omega$ while maintaining a 4D Poincaré-invariant induced metric in certain regions. The results also reveal Lorentz-violating propagation of gravitational signals due to the asymmetric warping, with the speed of gravity $c_{\rm grav}$ depending on the brane location and bulk parameters, offering testable implications for gravitational-wave phenomenology and brane cosmology. Overall, the framework connects string-inspired bulk fields to brane cosmology, providing avenues to address the cosmological constant problem and to explore observable consequences of bulk-induced Lorentz violation.

Abstract

We construct an n+q+2 dimensional background that has dilatonic q-brane singularities and that is charged under an antisymmetric tensor field, the background spacetime being maximally symmetric in n-dimensions with constant curvature k=0,+1,-1. For k=1 the bulk solutions correspond to black q-branes. For k=0,-1 the geometry resembles the `white hole' region of the Reissner-N"ordstrom solution with a past Cauchy horizon. The metric between the (timelike) singularity and the horizon is static whereas beyond the horizon it is cosmological. In the particular case of q=0, we study the motion of a codimension one n-brane in these charged dilatonic backgrounds that interpolate between the original scalar self-tuning and the black hole geometry and provide a way to avoid the naked singularity problem and/or the need of having exotic matter on the brane. These backgrounds are asymmetrically warped and so break 4D Lorentz symmetry in a way that is safe for particle physics but may lead to faster than light propagation in the gravitational sector.