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SimpleBounce : a simple package for the false vacuum decay

Ryosuke Sato

TL;DR

This work introduces SimpleBounce, a C++ package for computing the bounce solution in false vacuum decay using a gradient-flow-based reduction that minimizes the kinetic energy at fixed negative potential energy. The bounce is recovered by a scale transformation of the flow’s fixed point, leveraging the Coleman–Glaser–Martin framework for stable numerics. The approach yields fast, stable calculations for models with $1 \le n_\phi \le 8$, achieving ~0.1% accuracy in ~0.1 s, and is validated against CosmoTransitions with competitive or superior speed. Through detailed samples, benchmarks, and parameter studies, the paper demonstrates practical utility for multi-field decay analyses and provides a ready-to-use software package with documentation and example codes.

Abstract

We present SimpleBounce, a C++ package for finding the bounce solution for the false vacuum decay. This package is based on a flow equation which is proposed by the author and solves Coleman-Glaser-Martin's reduced problem: the minimization problem of the kinetic energy while fixing the potential energy. The bounce configuration is obtained by a scale transformation of the solution of this problem. For models with 1--8 scalar field(s), the bounce action can be calculated with O(0.1) % accuracy in O(0.1) s. This package is available at https://github.com/rsato64/SimpleBounce.

SimpleBounce : a simple package for the false vacuum decay

TL;DR

This work introduces SimpleBounce, a C++ package for computing the bounce solution in false vacuum decay using a gradient-flow-based reduction that minimizes the kinetic energy at fixed negative potential energy. The bounce is recovered by a scale transformation of the flow’s fixed point, leveraging the Coleman–Glaser–Martin framework for stable numerics. The approach yields fast, stable calculations for models with , achieving ~0.1% accuracy in ~0.1 s, and is validated against CosmoTransitions with competitive or superior speed. Through detailed samples, benchmarks, and parameter studies, the paper demonstrates practical utility for multi-field decay analyses and provides a ready-to-use software package with documentation and example codes.

Abstract

We present SimpleBounce, a C++ package for finding the bounce solution for the false vacuum decay. This package is based on a flow equation which is proposed by the author and solves Coleman-Glaser-Martin's reduced problem: the minimization problem of the kinetic energy while fixing the potential energy. The bounce configuration is obtained by a scale transformation of the solution of this problem. For models with 1--8 scalar field(s), the bounce action can be calculated with O(0.1) % accuracy in O(0.1) s. This package is available at https://github.com/rsato64/SimpleBounce.

Paper Structure

This paper contains 8 sections, 11 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Formulation
  3. Algorithm
  4. User instructions
  5. Sample codes and discussions
  6. Sample code for single scalar field model
  7. The Euclidean action for benchmark models
  8. Changing $n$ and $\tau_1$

Figures (2)

  • Figure 1: Flow chart of the algorithm of SimpleBounce. The default values of $\tau_0$ and $\tau_1$ are 0.05 and 0.4.
  • Figure 2: The runtime of the value of ${\cal S}_E$ for different number of the lattice $n$ and the flow time $\tau_1$. We take the model #8 in Tab. 1 of Athron:2019nbd. The environment of PC is same as Tab. \ref{['tab:performance']}.