The number of negative modes of the oscillating bounces

TL;DR

This paper investigates the spectrum of small perturbations around oscillating bounce solutions, confirming that a bounce with N nodes has exactly N negative modes, which clarifies their relation to false vacuum decay.

Contribution

It provides a rigorous analysis of the negative modes in oscillating bounce solutions, establishing a direct correspondence between the number of nodes and negative modes.

Findings

Bounce with N nodes has exactly N negative modes

More than one negative mode complicates the interpretation of false vacuum decay

Supports intuitive understanding of oscillating bounce spectra

Abstract

The spectrum of small perturbations about oscillating bounce solutions recently discussed in the literature is investigated. Our study supports quite intuitive and expected result: the bounce with N nodes has exactly N homogeneous negative modes. Existence of more than one negative modes makes obscure the relation of these oscillating bounce solutions to the false vacuum decay processes.