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

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Abstract
We consider the brane world picture in the context of higherderivative theories of gravity and tackle the problematic issues finetuning and braneembedding. First, we give an overview of extradimensional physics, from the KaluzaKlein 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 RandallSundrum 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 selfconsistent solutions for quadratic potentials of the fields. This gives us the tools to investigate higherderivative gravity theories in brane world models. Specifically, we take gravitational Lagrangians that depend on an arbitrary function of the Ricci scalar only, socalled $f(R)$gravity. We make use of the conformal equivalence between $f(R)$gravity and EinsteinHilbert gravity with an auxiliary scalar field. We find that the solutions in the higherderivative gravity framework behave very differently from the original RandallSundrum 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 finetuning problem. We address the issue of braneembedding, 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 higherderivative 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:  Thesis (Dissertation, LMU Munich) 

Keywords:  gravitation, brane worlds, higherderivative gravity, scalar field 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  2. May 2005 
1. Referee:  Mukhanov, Viatcheslav 
Persistent Identifier (URN):  urn:nbn:de:bvb:1936343 
MD5 Checksum of the PDFfile:  4b829e6686d9b7fa6eb79618f2ad4f85 
Signature of the printed copy:  0001/UMC 14578 
ID Code:  3634 
Deposited On:  02. Jun 2005 
Last Modified:  16. Oct 2012 07:49 