# Approximating tunneling rates in multi-dimensional field spaces

## TL;DR

This paper introduces a simplified method to estimate tunneling rates in multi-dimensional field spaces by reducing the problem to a one-field scenario, facilitating faster calculations of vacuum decay in complex models.

## Contribution

The authors propose a novel approximation technique that simplifies multi-field tunneling rate calculations to a one-field problem, validated with their code 'Anybubble.'

## Key findings

- The approximation accurately predicts tunneling rates across various potentials.
- It significantly reduces computational complexity in vacuum decay calculations.
- Validation shows good agreement with more detailed methods.

## Abstract

Quantum mechanics makes the otherwise stable vacua of a theory metastable through the nucleation of bubbles of the new vacuum. This in turn causes a first order phase transition. These cosmological phase transitions may have played an important role in settling our universe into its current vacuum, and they may also happen in future. The most important frameworks where vacuum decay happens contain a large number of fields. Unfortunately, calculating the tunneling rates in these models is very time-consuming. In this paper we present a simple approximation for the tunneling rate by reducing it to a one-field problem which is easy to calculate. We demonstrate the validity of this approximation using our recent code "Anybubble" for several classes of potentials.