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Applications of a Scalar Field to de Sitter Quantum Gravity and to HoravaLifshitz Gravity

 Author / Creator
 Wu, Xing

In the first part of the thesis, we study the minimallycoupled massless scalar field in de Sitter spacetime. Because of the nonlinear nature of general relativity, the direct analysis of the graviton is very complicated. So, we use the scalar field as an analogue to the graviton, and shift invariance as an analogue to gauge invariance of the graviton. Physical observables are restricted to those with shift invariance. Starting from a massive scalar field in the Euclidean vacuum, we take the massless limit of the Wightman function in this state. We propose to use this twopoint function in the massless limit with the divergent part dropped off as an intermediate tool to calculate twopoint functions of physical operators. Examples for the twopoint functions of gradients of the field and for the npoint products of the differences of the field values are calculated. We find that as long as one considers only shiftinvariant operators, there does exist a welldefined vacuum state, and the correlation functions are free of IR divergences and exhibit the cluster decomposition property. This suggests that there should exist a de Sitterinvariant vacuum for the graviton on de Sitter, as long as one considers only gauge invariant operators. In the second part, we study vacuum static solutions with spherical symmetry in the IR limit of HoravaLifshitz gravity. In this case, the problem can be greatly simplified by using a trick to project the 4D theory into a 3D massless scalar field minimally coupled to 3D Euclidean gravity. Then the solution to HoravaLifshitz gravity can be generated from the Schwarzschild solution in general relativity by a constant rescaling of the 3D scalar field, though this is in general not a black hole solution. This solution has a naked singularity and should be regarded as the exterior to some spherical distribution of matter. The nontrivial parameter (i.e. the parameter of the theory, not the integration constant) of the solution is constrained by physical considerations. In particular, using the correspondence between the IR limit of HoravaLifshitz and Einsteinaether theory, it is also constrained by conditions arising from the latter.

 Subjects / Keywords

 Graduation date
 201306

 Type of Item
 Thesis

 Degree
 Doctor of Philosophy

 License
 This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for noncommercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.