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Applications of a Scalar Field to de Sitter Quantum Gravity and to Horava-Lifshitz Gravity Open Access


Other title
quantum field theory
de Sitter
Horava-Lifshitz gravity
Type of item
Degree grantor
University of Alberta
Author or creator
Wu, Xing
Supervisor and department
Page, Don N. (Physics)
Examining committee member and department
Frolov, Valeri (Physics)
Pogosyan, Dmitri (Physics)
Morsink, Sharon (Physics)
Doran, Charlse (Mathematics)
Cai, Rong-Gen (ITP, CAS)
Department of Physics

Date accepted
Graduation date
Doctor of Philosophy
Degree level
In the first part of the thesis, we study the minimally-coupled massless scalar field in de Sitter spacetime. Because of the non-linear 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 two-point function in the massless limit with the divergent part dropped off as an intermediate tool to calculate two-point functions of physical operators. Examples for the two-point functions of gradients of the field and for the n-point products of the differences of the field values are calculated. We find that as long as one considers only shift-invariant operators, there does exist a well-defined 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 Sitter-invariant 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 Horava-Lifshitz 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 Horava-Lifshitz 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 Horava-Lifshitz and Einstein-aether theory, it is also constrained by conditions arising from the latter.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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