Scalar fields and higher-derivative gravity in brane worlds

We consider the brane world picture in the context of
higher-derivative theories of gravity and tackle the problematic
issues fine-tuning and brane-embedding. First, we give an overview
of extra-dimensional physics, from the Kaluza-Klein picture up to
modern brane worlds with large extra dimensions. We describe the
different models and their physical impact on future experiments.
We work within the framework of Randall-Sundrum models in which the
brane is a gravitating object, which warps the background metric.
We add scalar fields to the original model and find new and
self-consistent solutions for quadratic potentials of the fields.
This gives us the tools to investigate higher-derivative gravity
theories in brane world models. Specifically, we take gravitational
Lagrangians that depend on an arbitrary function of the Ricci
scalar only, so-called $f(R)$-gravity. We make use of the conformal
equivalence between $f(R)$-gravity and Einstein-Hilbert gravity
with an auxiliary scalar field. We find that the solutions in the
higher-derivative gravity framework behave very differently from
the original Randall-Sundrum model: the metric functions do not
have the typical kink across the brane. Furthermore, we present
solutions that do not rely on a cosmological constant in the bulk
and so avoid the fine-tuning problem. We address the issue of
brane-embedding, which is important in perturbative analyses. We
consider the embedding of codimension one hypersurfaces in general
and derive a new equation of motion with which the choice for the
embedding has to comply. In particular, this allows for a
consistent consideration of brane world perturbations in the case
of higher-derivative gravity. We use the newly found background
solutions for quadratic potentials and find that gravity is still
effectively localized on the brane, i.e that the Newtonian limit
holds.