A quantum theory of gravity remains one of the greatest challenges of contemporary physics. It is well established that a perturbative treatment of gravity as a quantum field theory leads to a non-renormalisable setup. However gravity could still exist as a consistent and predictive quantum field theory on a non-perturbative level. This is explored in the asymptotic safety scenario which was initially proposed by S. Weinberg. In this thesis we investigate the ultraviolet behaviour of gravity within the asymptotic safety conjecture and discuss phenomenological implications. We start out by introducing the concept of the functional renormalisation group and its application to gravity. This non-perturbative tool is the technical basis for our investigation of a template quantum gravity action, namely a function f(R) in the Ricci scalar in four dimensions. We compute exact fixed point solutions to very high polynomial orders via the development of a dedicated high performance code. The picture of an interacting UV fixed point that receives only small quantitative corrections from higher derivative operators is confirmed and extended. The results are then expanded to include minimally coupled matter fields and we investigate the matter effects on the gravitational fixed point. We determine regimes of compatibility in the vicinity of the purely gravitational setup but also find constraints on the number of matter fields. Finally we look at the phenomenological implications of a running Newton's coupling, one of the key features of the asymptotic safety setup, to graviton-mediated eikonal scattering amplitudes. In this kinematic regime we investigate the possibility of a TeV-sized fundamental Planck mass via the introduction of compact extra dimensions. We identify the fingerprints of asymptotic safety in the t-channel scattering amplitude and find crucial differences compared to semi-classical computations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:655545 |
| Date | January 2015 |
| Creators | Schröder, Jan |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://sro.sussex.ac.uk/id/eprint/54172/ |
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