Oscillating instantons as homogeneous tunneling channels

TL;DR

This paper investigates oscillating instantons in Einstein gravity with scalar fields, demonstrating their existence, higher tunneling probabilities, and significance as homogeneous tunneling channels in vacuum decay scenarios.

Contribution

It introduces the concept of oscillating instantons as homogeneous tunneling channels and analyzes their conditions and probabilities, expanding understanding of vacuum decay mechanisms.

Findings

Oscillating instantons exist under specific potential conditions.

Their tunneling probabilities surpass Hawking-Moss instantons.

They are comparable to Coleman-DeLuccia channels in certain cases.

Abstract

In this paper, we study Einstein gravity with a minimally coupled scalar field accompanied with a potential, assuming an O(4) symmetric metric ansatz. We call an Euclidean instanton is to be an oscillating instanton, if there exists a point where the derivative of the scale factor and the scalar field vanish at the same time. Then we can prove that the oscillating instanton can be analytically continued, both as inhomogeneous and homogeneous tunneling channels. Here, we especially focus on the possibility of a homogeneous tunneling channel. For the existence of such an instanton, we have to assume three things: (1) there should be a local maximum and the curvature of the maximum should be sufficiently large, (2) there should be a local minimum and (3) the other side of the potential should have a sufficiently deeper vacuum. Then, we can show that there exists a number of oscillating instanton solutions and their probabilities are higher compared to the Hawking-Moss instantons. We also check the possibility when the oscillating instantons are comparable with the Coleman-DeLuccia channels. Thus, for a general vacuum decay problem, we should not ignore the oscillating instanton channels.