Scalar-Tensor Gravity on a Gauss-Bonnet Brane World

Abstract

The effective four-dimensional, linearised gravity for a brane world model with higher order curvature terms and a bulk scalar field is analysed. Large and small distance gravitational laws are derived. The model has a single brane embedded in a five-dimensional bulk spacetime, and the scalar field represents the dilaton or a moduli field. The quadratic, Gauss-Bonnet curvature term (and corresponding higher kinetic terms for the scalar) is also included in the bulk action. It is particularly natural to include such terms in a brane world model. Boundary terms and junction conditions for the higher order terms are given. The extra terms allow additional solutions of the field equations, which give better agreement with observational constraints. Brans-Dicke gravity is obtained on the brane. The scalar and tensor perturbations are affected differently by the higher gravity terms, and this provides a way for the scalar modes to be suppressed relative to the tensor ones. Another new (but less useful) feature is the appearance of instabilities for some parameter ranges.