# Towards the fate of the oscillating false vacuum

## TL;DR

This paper investigates quantum tunnelling from an oscillating false vacuum state in quantum field theory, providing analytical and numerical estimates of tunnelling probabilities and criteria for bubble growth or collapse.

## Contribution

It introduces a novel analysis of tunnelling from oscillating initial states and offers criteria to predict bubble evolution post-tunnelling.

## Key findings

- Analytical and numerical estimates of tunnelling probabilities.
- Criteria to distinguish bubble growth from collapse.
- Insights into phase transition dynamics in oscillating vacua.

## Abstract

Motivated by cosmological examples we study quantum field theoretical tunnelling from an initial state where the "classical field", i.e. the vacuum expectation value of the field operator is spatially homogeneous but performing a time-dependent oscillation about a local minimum. In particular we estimate both analytically and numerically the exponential contribution to the tunnelling probability. We additionally show that after the tunnelling event, the classical field solution - the so-called "bubble" - mediating the phase transition can either grow or collapse. We present a simple analytical criterium to distinguish between the two behaviours.