Alternative theories of gravity and their application to cosmology

In this thesis we study extended theories of gravity in the context of cosmology. The first part is dedicated to the application of the theory of dynamical systems, which allow us to investigate the global dynamics of some cosmological models resulting from scalar-tensor and higher-order theories of gravity. We use the dynamical systems approach with non–compact expansion normalised variables to study the isotropisation of Bianchi type I models in Rn–gravity. We find that these type of models can isotropise faster or slower than their general relativity counterparts. We extend this analysis to the full class of orthogonal spatially homogeneous Bianchi models to study the effect of spatial curvature on the isotropisation of these models. A compact state space is constructed by dividing the state space into different sectors, that allows us to also investigate static solutions and bouncing or recollapsing behaviours which is not possible when using non-compact expansion normalised variables. We find no Einstein static solutions, but there do exist cosmologies with bounce behaviours. We also find that all isotropic points are flat Friedmann like. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We next study the phase-space of Friedmann models derived from scalar-tensor gravity where the non-minimal coupling is F(φ) = ξφ2 and the self-interaction potential is V (φ) = λφn. Transient almost-Friedmann phases evolving towards accelerated expansion and unstable inflationary phases evolving towards stable ones are found. In the last part of this work, we set out a framework to analyse tensor anisotropies in the cosmic microwave background of scalar-tensor cosmologies. As an example, we consider one of the exact solutions found for the class of scalar-tensor theories considered above.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2008

Author dc:creator

• Leach, Jannie A

Advisor dc:contributor.advisor

• Bruyns, Peter

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/4901

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/4901