Vacuum Decay Induced by Quantum Fluctuations

TL;DR

This paper investigates how quantum field fluctuations can induce vacuum decay in a scalar field, revealing that certain large fluctuations can significantly enhance decay rates beyond traditional tunneling mechanisms.

Contribution

It introduces a detailed analysis of quantum fluctuation effects on vacuum decay, highlighting the dominant role of quadratic operator fluctuations over linear ones and tunneling.

Findings

Quadratic fluctuations lead to much higher decay rates than tunneling.

Large fluctuations in quadratic operators can dominate vacuum decay.

Linear fluctuations and tunneling contribute comparably, but quadratic fluctuations are most significant.

Abstract

We treat the effects of quantum field fluctuations on the decay of a meta-stable state of a self-coupled scalar field. We consider two varieties of field fluctuations and their potential effects in a semiclassical description. The first are the fluctuations of the time derivative a free massive scalar field operator, which has been averaged over finite regions of space and time. These fluctuations obey a Gaussian probability distribution. A sufficiently large fluctuation is assumed to produce an effect analogous to a classical initial field velocity, which can cause a finite region to fly over the barrier separating the meta-stable state from the stable vacuum state. Here we find a contribution to the decay rate which is comparable to the decay rate by quantum tunneling, as computed in an instanton approximation. This result is consistent with those of other authors. We next consider the effects of the fluctuations of operators which are quadratic in the time derivative of the free scalar field. The quadratic operator is also averaged over finite regions of space and of time. Now the probability distribution for the averaged operator falls more slowly than an exponential function, allowing for the possibility of very large fluctuations. We find a contribution to the decay rate which is much larger than those coming from either quantum tunneling or linear field fluctuations, and hence appears to be the dominant decay mechanism.