Self Excitation of the Tunneling Scalar Field in False Vacuum Decay

TL;DR

This paper develops an analytical method to analyze the quantum excitation spectrum of a scalar field during false vacuum decay, revealing how the potential shape influences particle creation phenomena.

Contribution

It introduces a concise analytical approach to determine the quantum state after bubble nucleation, highlighting the impact of potential shape on excitation spectra.

Findings

Excitation spectrum strongly depends on the potential shape.

Analytical treatment achieved for piece-wise quadratic potentials.

Features of the spectrum are discussed for general tunneling potentials.

Abstract

A method to determine the quantum state of a scalar field after $O(4)$-symmetric bubble nucleation has been developed recently. The method has an advantage that it concisely gives us a clear picture of the resultant quantum state. In particular, one may interpret the excitations as a particle creation phenomenon just as in the case of particle creation in curved spacetime. As an application, we investigate in detail the spectrum of quantum excitations of the tunneling field when it undergoes false vacuum decay. We consider a tunneling potential which is piece-wise quadratic, hence is simple enough to allow us an analytical treatment. We find a strong dependence of the excitation spectrum upon the shape of the potential on the true vacuum side. We then discuss features of the excitation spectrum common to general tunneling potentials not restricted to our simple model.