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

Abstract

We present a study of the vacuum transition probabilities taking into account quantum corrections. We first introduce a general method that expands previous works employing the Lorentzian formalism of the Wheeler-De Witt equation by considering higher order terms in the semiclassical expansion. The method presented is applicable in principle to any model in the minisuperspace and up to any desired order in the quantum correction terms. Then, we apply this method to obtain analytical solutions for the probabilities up to second quantum corrections for homogeneous isotropic and anisotropic universes. We use the Friedmann-Lemaitre-Robertson-Walker metric with positive and zero curvature for the isotropic case and the Bianchi III and Kantowski-Sachs metrics for the anisotropic case. Interpreting the results as distribution probabilities of creating universes by vacuum decay with a given size, we found that the general behaviour is that considering up to the second quantum correction leads to an avoidance of the initial singularity. However, we show that this result can only be achieved for the isotropic universe. Furthermore, we also study the effect of anisotropy on the transition probabilities.

arXiv comment37 pages, 4 figures, clarifications and references added, typos corrected

References in corpus (32)

• The Dynamics of General Relativity
• Quantum Gravity: a Progress Report
• Evidence for anisotropy of cosmic acceleration
• Bianchi type III models with anisotropic dark energy
• Probing cosmic isotropy with a new X-ray galaxy cluster sample through the $L_{\text{X}}-T$ scaling relation
• A Holographic Framework for Eternal Inflation
• Holography of AdS vacuum bubbles
• Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology
• Negative mode problem in false vacuum decay with gravity
• False Vacuum Decay With Gravity in Non-Thin-Wall Limit
• Observations in Quantum Cosmology
• Lorentzian Vacuum Transitions: Open or Closed Universes?
• A Fresh Look at the Calculation of Tunneling Actions including Gravitational Effects
• Gauss-Bonnet Term on Vacuum Decay
• Study of the Inflationary Spectrum in the Presence of Quantum Gravity Corrections
• Quantum Transitions Between Minkowski and de Sitter Spacetimes
• Towards a Solution of the Negative Mode Problem in Quantum Tunnelling with Gravity
• Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation
• Quantum gravity corrections to the matter dynamics in the presence of a reference fluid
• Quantum Cosmology
• Revisiting Coleman-de Luccia transitions in the AdS regime using holography
• QFT in Curved Spacetime from Quantum Gravity: proper WKB decomposition of the gravitational component
• Exact Coleman-de Luccia Instantons
• Aspects of the negative mode problem in quantum tunneling with gravity
• Exactly Solvable Vacuum Decays with Gravity
• Vacuum Transitions in Two-Dimensions and their Holographic Interpretation
• Vacuum Decay Actions from Tunneling Potentials for General Spacetime Dimension
• Vacuum decay and bubble nucleation in $f(R)$ gravity
• Tunneling Potential Actions from Canonical Transformations
• Tunneling in Anisotropic Cosmological Models
• Revisiting Vacuum decay in Field Theory
• Lorentzian Vacuum Transitions with a Generalized Uncertainty Principle