Vibrations of thick domain walls: How to avoid no-go theorem

TL;DR

This paper investigates the vibrational properties of thick domain walls in cosmology, revealing conditions under which long-lived localized vibrations can exist, despite a no-go theorem on discrete spectrum levels.

Contribution

It demonstrates scenarios where long-lived vibrations occur on thick domain walls, challenging previous no-go theorems about their excitation spectra.

Findings

Long-lived localized vibrations can exist on thick domain walls.

The discrete spectrum of excitations is limited to zero (translational) modes.

These vibrations can influence interactions between multiple domain walls.

Abstract

The asymptotic properties of the stability potentials of kinks with power-law tails are discussed. In particular, in cosmology such kinks can describe "thick" domain walls. The discrete part of the domain wall excitation spectrum, the profile of which is described by a kink solution with one or both power-law asymptotics, cannot contain levels other than zero (translational) mode. Nevertheless, it can be shown that scenarios are quite possible when long-lived localized vibrations will be excited on the domain wall. This, in turn, can affect the processes of interaction of two or more domain walls.