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General Relativity and Quantum Cosmology

arXiv:2111.11571 (gr-qc)
[Submitted on 22 Nov 2021 (v1), last revised 28 Apr 2022 (this version, v3)]

Title:Lorentzian Vacuum Transitions in Hořava-Lifshitz Gravity

Authors:H. Garcia-Compean, D. Mata-Pacheco
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Abstract:The vacuum transition probabilities for a Friedmann-Lemaître-Robertson-Walker universe with positive curvature in Hořava-Lifshitz gravity in the presence of a scalar field potential in the Wentzel-Kramers-Brillouin approximation are studied. We use a general procedure to compute such transition probabilities using a Hamiltonian approach to the Wheeler-DeWitt equation presented in a previous work. We consider two situations of scalar fields, one in which the scalar field depends on all the spacetime variables and other in which the scalar field depends only on the time variable. In both cases analytic expressions for the vacuum transition probabilities are obtained and the infrared and ultraviolet limits are discussed for comparison with the result obtained by using general relativity. For the case in which the scalar field depends on all spacetime variables we obtain that in the infrared limit it is possible to obtain a similar behavior as in general relativity, however in the ultraviolet limit the behavior found is completely opposite. Some few comments about possible phenomenological implications of our results are given. One of them is a plausible resolution of the initial singularity. On the other hand for the case in which the scalar field depends only on the time variable, the behavior coincides with that of general relativity in both limits, although in the intermediate region the probability is slightly altered.
Comments: 26 pages, 2 figures. Some references added
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:2111.11571 [gr-qc]
  (or arXiv:2111.11571v3 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.2111.11571
Related DOI: https://doi.org/10.3390/universe8040237

Submission history

From: Daniel Mata-Pacheco [view email]
[v1] Mon, 22 Nov 2021 23:22:10 UTC (121 KB)
[v2] Wed, 13 Apr 2022 00:07:20 UTC (122 KB)
[v3] Thu, 28 Apr 2022 23:13:28 UTC (122 KB)
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