# Tunneling Between Schwarzschild-de Sitter Vacua

## TL;DR

This paper investigates how static primordial black holes influence vacuum decay rates between different cosmological constant states, highlighting the importance of black holes and initial cosmological constants in transition processes.

## Contribution

It extends the analysis of vacuum decay by comparing tunneling rates in Schwarzschild-de Sitter backgrounds using numerical thin wall instantons for various nucleation scenarios.

## Key findings

- Black holes increase vacuum transition rates when combined with a cosmological constant.
- The most probable outcome is the elimination of inhomogeneities in the final vacuum state.
- Including both black holes and a cosmological constant is necessary to enhance transition probabilities.

## Abstract

We extend the study of the effect of static primordial black holes on vacuum decay. In particular, we compare the tunneling rates between vacua of different values of the cosmological constant and black hole mass by pointing out the dominant processes based on a numerical examination of the thin wall instanton. Three distinct cases are considered, namely the nucleation of a true vacuum bubble into the false vacuum, the nucleation of a false vacuum bubble into the true vacuum as well as the Farhi-Guth-Guven mechanism. As a proof of concept, it is shown that in order to increase the transition rate into an inflating region, we find that not only is the inclusion of a black hole necessary, but the inclusion of a cosmological constant in the initial phase is also required. Among the cases studied, we show that the most likely scenario is the elimination of inhomogeneities in the final phase.