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

TL;DR

This paper develops a method to incorporate higher-order quantum corrections into Lorentzian vacuum transition probabilities in gravity, revealing that second-order corrections can prevent initial singularities in isotropic universes.

Contribution

It introduces a general semiclassical expansion method for vacuum transition probabilities applicable to various models and computes analytical solutions up to second quantum corrections.

Findings

Second quantum corrections can avoid initial singularities in isotropic universes.

Anisotropy influences the vacuum transition probabilities.

The method is applicable to different minisuperspace models.

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.