Scalar fields and higher-derivative gravity in brane worlds

Pichler, Sebastian (2005): Scalar fields and higher-derivative gravity in brane worlds. Dissertation, LMU München: Faculty of Physics

Abstract

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.

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: gravitation, brane worlds, higher-derivative gravity, scalar field
• Subjects: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 530 Physics
• Faculties: Faculty of Physics
• Language: English
• Date of oral examination: 2. May 2005
• 1. Referee: Mukhanov, Viatcheslav
• Signature of the printed copy: 0001/UMC 14578