Parametrized Path Approach to Vacuum Decay

TL;DR

This paper introduces a novel real-time method for analyzing vacuum decay by reducing the problem to a finite set of degrees of freedom and solving a generalized Schrödinger equation, offering new insights into decay dynamics.

Contribution

It presents a new approach to vacuum decay analysis that differs from instanton methods, applicable to scalar fields and cold atom models, with plans to include gravity.

Findings

Decay is faster at early times compared to instanton predictions.

Method successfully applied to scalar field in Minkowski space.

Potential extension to include gravitational effects.

Abstract

We develop a new real-time approach to vacuum decay based on a reduction to a finite number of degrees of freedom. The dynamics is followed by solving a generalized Schr\"odinger equation. We first apply this method to a real scalar field in Minkowski space and compare the decay rate with that obtained by the instanton approach. The main difference is in the early-time dynamics, where the decay is faster due to the tail of the wave function. We then apply it to a cold atom model recently proposed to simulate vacuum decay experimentally. This approach will be extended to include gravity in a future work.