What determines the rest frame of bubble nucleation?

TL;DR

This paper investigates the rest frame of bubble nucleation in a false vacuum, demonstrating that the initial conditions of electric field activation do not influence the nucleation rest frame, contrary to prior assumptions based on idealized models.

Contribution

It provides a more realistic analysis of bubble nucleation, showing the robustness of the nucleation rest frame against the electric field activation process.

Findings

The nucleation rest frame remains unaffected as the electric field activation time approaches negative infinity.

The process of turning on the electric field influences the resulting electric current and charge density.

The conclusions of previous idealized models are validated in more realistic scenarios.

Abstract

We revisit the question addressed in recent papers by Garriga et al: What determines the rest frame of pair nucleation in a constant electric field? The conclusion reached in these papers is that pairs are observed to nucleate at rest in the rest frame of the detector which is used to detect the pairs. A similar conclusion should apply to bubble nucleation in a false vacuum. This conclusion however is subject to doubt due to the unphysical nature of the model of a constant eternal electric field that was used by Garriga et al. The number density of pairs in such a field would be infinite at any finite time. Here we address the same question in a more realistic model where the electric field is turned on at a finite time $t_0$ in the past. The process of turning on the field breaks the Lorentz invariance of the model and could in principle influence the frame of pair nucleation. We find however that the conclusion of Garriga et al still holds in the limit $t_0 \to -\infty$. This shows that the setup process of the electric field does not have a lasting effect on the observed rest frame of pair nucleation. {On the other hand, the electric current and charge density due to the pairs are determined by the way in which the electric field was turned on.