Tunneling from a Minkowski vacuum to an AdS vacuum: A new thin-wall regime

TL;DR

This paper investigates quantum tunneling from a Minkowski to an anti-de Sitter vacuum, revealing a new thin-wall regime influenced by strong gravitational effects and providing a simplified method to determine vacuum stability boundaries.

Contribution

The study introduces a novel thin-wall tunneling regime under strong gravity and offers a simple computational approach to identify stability regions in parameter space.

Findings

Strong gravity can completely suppress tunneling in certain potentials.

A new type of thin-wall bounce occurs when vacuum energy differences are large.

A simple overshoot/undershoot method determines the stability boundary.

Abstract

Using numerical and analytic methods, we study quantum tunneling from a Minkowski false vacuum to an anti-de Sitter true vacuum. Scanning the parameter space of theories with quartic and non-polynomial potentials, we find that for any given potential tunneling is completely quenched if gravitational effects are made sufficiently strong. For potentials where $\epsilon$, the energy density difference between the vacua, is small compared to the barrier height, this occurs in the thin-wall regime studied by Coleman and De Luccia. However, we find that other potentials, possibly with $\epsilon$ much greater than the barrier height, produce a new type of thin-wall bounce when gravitational effects become strong. We show that the critical curve that bounds the region in parameter space where the false vacuum is stable can be found by a computationally simple overshoot/undershoot argument. We discuss the treatment of boundary terms in the bounce calculation and show that, with proper regularization, one obtains an identical finite result for the tunneling exponent regardless of whether or not these are included. Finally, we briefly discuss the extension of our results to transitions between anti-de Sitter vacua.