Lorentzian Vacuum Transitions with a Generalized Uncertainty Principle

Abstract

The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel-Kramers-Brillouin approximation. First we propose a method to compute these transition probabilities by solving the Wheeler-DeWitt equation in a semi-classical approach for any model of superspace that contains terms of squared as well as linear momenta in the Hamiltonian constraint generalizing in this way previous results. Then we apply this method to compute the transition probabilities for a Friedmann-Lemaitre-Robertson-Walker metric with positive and null curvature and for the Bianchi III metric when the coordinates of minisuperspace obey a Standard Uncertainty Principle and when a Generalized Uncertainty Principle is taken into account. In all cases we compare the results and found that the effect of considering a Generalized Uncertainty Principle is that the probability is enhanced at first but it decays faster so when the corresponding scale factor is big enough the probability is reduced. We also consider the effect of anisotropy and compare the result of the Bianchi III metric with the flat FLRW metric which corresponds to its isotropy limit and comment the differences with previous works.

33 pages, 3 figures. All sections were improved. Section 6 added. References added

References in corpus (15)

• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• GUP parameter from quantum corrections to the Newtonian potential
• Probing cosmic isotropy with a new X-ray galaxy cluster sample through the $L_{\text{X}}-T$ scaling relation
• Does Hubble Tension Signal a Breakdown in FLRW Cosmology?
• Cosmological implications of the anisotropy of ten galaxy cluster scaling relations
• Hints of FLRW Breakdown from Supernovae
• The Most General Form of Deformation of the Heisenberg Algebra from the Generalized Uncertainty Principle
• Generalized uncertainty principle in Bianchi type I quantum cosmology
• Deformation of the Wheeler-DeWitt Equation
• Introductory Lectures on Quantum Cosmology (1990)
• Cosmology with minimal length uncertainty relations
• Deformation of Second and Third Quantization
• Generalized Uncertainty Principle effects in the Hořava-Lifshitz quantum theory of gravity
• Quantum gravity and quantum probability
• Polychronic Tunneling: New Tunneling Processes Experiencing Euclidean and Lorentzian Evolution Simultaneously

Cited by in corpus (1)

• Effects of quantum corrections to Lorentzian vacuum transitions in the presence of gravity