Lorentzian Vacuum Transitions for Anisotropic Universes

TL;DR

This paper extends the study of vacuum transition probabilities to anisotropic universes using a Lorentzian Hamiltonian approach, providing a general method applicable to various cosmological models and analyzing the impact of anisotropy on decay rates.

Contribution

It introduces a general procedure to compute vacuum decay rates in anisotropic universes, expanding previous isotropic analyses to include multiple anisotropic metrics.

Findings

Transition probabilities decrease with increasing anisotropy in Bianchi III.

The formalism reproduces known isotropic results for FLRW universes.

Conditions relate degrees of freedom to simplify probability descriptions.

Abstract

The vacuum transition probabilities for anisotropic universes in the presence of a scalar field potential in the Wentzel-Kramers-Brillouin approximation are studied. We follow the work by Cespedes et al [Phys. Rev. D 104, 026013 (2021)], which discuss these transitions in the isotropic context using the Wheeler-DeWitt equation, the Lorentzian Hamiltonian approach and the thin wall limit. First, we propose a general procedure to adapt their formalism to compute the decay rates for any superspace model. Then we apply it to compute the transition probabilities of an Friedmann-Lemaitre-Robertson-Walker (FLRW) metric with both positive and zero curvature, reproducing in this way one of the results obtained at Cespedes et al. We then proceed to apply the formalism to three anisotropic metrics, namely, Kantowski-Sachs, Bianchi III and biaxial Bianchi IX to compute the rate decays for these three cases. In the process we find that this method involves some conditions which relates the effective number of independent degrees of freedom resulting on all probabilities being described with only two independent variables. For the Bianchi III metric, we find that a general effect of anisotropy is to decrease the transition probability as the degree of anisotropy is increased, having as the isotropic limit the flat FLRW result.