Since the beginning of the 20th century, much time and effort has been invested in the search for a theory of quantum gravity. While this provided a myriad of possibilities, it has so far failed to find a definitive answer. Here we take an alternative approach: instead of constructing a theory of quantum gravity and examining its low energy limit, we start with the conventional theory and ask what are the first deviations induced by a possible quantization of gravity. It is proposed that in this limit quantum gravity, whatever the ultimate theory might be, manifests itself as non-locality. In this thesis are explored two different approaches to effective theories. In the first, it is demonstrated how combining quantum field theory with general relativity naturally gives rise to non-locality. This is explored in the context of inflation, a natural place to look for high energy phenomena. By considering a simple scalar field theory, it is shown how non-locality results in higher dimensional operators and what the effects are on inflationary models. The second approach looks at a theory which naturally incorporates a minimal scale. Noncommutative geometry parallels the phase space or deformation quantization approach of quantum mechanics. It supposes that at short scales, the structure of spacetime is algebraic rather than geometric. In the first instance, we follow the first section and look at cosmological implications by replacing normal scalar theory with its noncommutative counterpart. In the second, we take a step back and examine the implications of quantization on the differential geometry. The formalism is developed and applied to generic spherically symmetric spacetimes where it is shown that to first order in deformation, the quantization is unique.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:759573 |
| Date | January 2018 |
| Creators | Fritz, Christopher |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://sro.sussex.ac.uk/id/eprint/79185/ |
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