Scalar brane backgrounds in higher order curvature gravity

TL;DR

The paper analyzes maximally symmetric brane-world solutions in five dimensions with a bulk scalar and a Lovelock-type action that yields field equations with no higher than second order derivatives, including the Gauss-Bonnet term $\mathcal{L}_{\mathrm{GB}}$. It develops conformally flat bulk solutions, brane junction conditions, and a tensor perturbation framework to study gravity localisation, stability, and self-tuning. It demonstrates that higher-curvature corrections can induce ghosts and tachyons, complicating localization and self-tuning, and provides a detailed six-dimensional Kaluza-Klein example illustrating both potential gravity localisation and the ghost problem. The work clarifies the constraints and trade-offs when incorporating Gauss-Bonnet and scalar couplings into brane-world models and outlines analytic solution methods, highlighting how finite-volume and no-naked-singularity requirements constrain self-tuning. Overall, the results map the subtle balance between higher-curvature corrections, brane tension, and gravity localisation in string-inspired setups, and point to directions for further investigation of bulk ghosts and stability.

Abstract

We investigate maximally symmetric brane world solutions with a scalar field. Five-dimensional bulk gravity is described by a general lagrangian which yields field equations containing no higher than second order derivatives. This includes the Gauss-Bonnet combination for the graviton. Stability and gravitational properties of such solutions are considered, and we particularily emphasise the modifications induced by the higher order terms. In particular it is shown that higher curvature corrections to Einstein theory can give rise to instabilities in brane world solutions. A method for analytically obtaining the general solution for such actions is outlined. Genericaly, the requirement of a finite volume element together with the absence of a naked singularity in the bulk imposes fine-tuning of the brane tension. A model with a moduli scalar field is analysed in detail and we address questions of instability and non-singular self-tuning solutions. In particular, we discuss a case with a normalisable zero mode but infinite volume element.