# Bounce Configuration from Gradient Flow

## TL;DR

This paper introduces a novel gradient flow-based method to efficiently find bounce configurations in false vacuum decay scenarios, applicable to multi-field models, by modifying the flow to stabilize the bounce as a fixed point.

## Contribution

A new modified gradient flow technique that reliably locates bounce solutions as stable fixed points, simplifying the computational process in complex models.

## Key findings

- The modified flow converges to the bounce configuration in numerical tests.
- The method works for a large class of multi-field models.
- It avoids the need for careful initial guess selection.

## Abstract

Based on the gradient flow, we propose a new method to determine the bounce configuration for false vacuum decay. Our method is applicable to a large class of models with multiple fields. Since the bounce is a saddle point of an action, a naive gradient flow method which minimizes the action does not work. We point out that a simple modification of the flow equation can make the bounce its stable fixed point while the false vacuum configuration an unstable one. Consequently, the bounce configuration can be obtained simply by following the flow without a careful choice of an initial configuration. With numerical analysis, we confirm the validity of our claim, checking that the flow equation we propose indeed has solutions that flow into the bounce configuration.