Scalar brane backgrounds in higher order curvature gravity

TL;DR

This paper explores maximally symmetric brane world solutions in higher order curvature gravity with a scalar field, analyzing stability, gravitational properties, and the effects of higher curvature corrections, including potential instabilities and self-tuning solutions.

Contribution

It provides a general method for obtaining solutions in higher order curvature gravity theories and examines the stability and physical properties of these brane world models.

Findings

Higher curvature terms can induce instabilities in brane solutions.

Fine-tuning of brane tension is often required for finite volume and no singularities.

A detailed analysis of a scalar field model reveals conditions for stability and self-tuning.

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.