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

• Author / Creator

  Wu, Xing

• 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.

• Subjects / Keywords

  • De Sitter
  • Horava-Lifshitz gravity
  • Quantum field theory

• Graduation date

  Spring 2013

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3P604

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial 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.