# Aspects of the negative mode problem in quantum tunneling with gravity

## TL;DR

This paper investigates the longstanding negative mode problem in quantum tunneling with gravity, analyzing its occurrence across different potentials and showing it can arise at energies below the Planck scale, with implications for vacuum decay stability.

## Contribution

The study provides a detailed analysis of the negative mode problem using numerical and analytical methods, revealing its dependence on potential types and energy scales, especially in Higgs-like potentials.

## Key findings

- Negative modes can occur at energies below the Planck scale for polynomial potentials.
- In Higgs-like potentials, negative modes appear only at the Planck scale.
- The negative mode problem is not inherently tied to Planck-scale physics.

## Abstract

Some solutions describing vacuum decay exhibit a catastrophic instability. This, so-called negative mode problem in quantum tunneling with gravity, was discovered 34 years ago and in spite of the fact that in these years many different groups worked on this topic, it has still not been resolved. Here, we briefly summarize the current status of the problem and investigate properties of the bounces, numerically and analytically for physically interesting potentials. In the framework of the Hamiltonian approach we show that for generic polynomial potentials the negative mode problem could arise at energies much lower than the Planck mass, indicating that the negative mode problem is not related to physics at the Planck scale. At the same time we find that for a Higgs like potential, as it appears in the standard model, the problem does not appear at realistic values of the potential's parameters but only at the Planck scale.