# Flyover vacuum decay

## TL;DR

This paper investigates the stochastic approach to vacuum decay, showing that flyover transitions often resemble tunneling but can be significantly faster in certain cases, challenging traditional views of de Sitter space.

## Contribution

It demonstrates that flyover vacuum decay rates are similar to tunneling rates, except for upward transitions, which can be much faster, revealing new dynamics in vacuum decay processes.

## Key findings

- Flyover transition rates match tunneling rates in most cases.
- Upward de Sitter transitions can be orders of magnitude faster than tunneling.
- Bubble nucleation dynamics differ from standard models, especially in flat space and upward transitions.

## Abstract

We use analytic estimates and numerical simulations to explore the stochastic approach to vacuum decay. According to this approach, the time derivative of a scalar field, which is in a local vacuum state, develops a large fluctuation and the field \flies over" a potential barrier to another vacuum. The probability distribution for the initial fluctuation is found quantum mechanically, while the subsequent nonlinear evolution is determined by classical dynamics. We find in a variety of cases that the rate of such flyover transitions has the same parametric form as that of tunneling transitions calculated using the instanton method, differing only by a numerical factor O(1) in the exponent. An important exception is an "upward" transition from a de Sitter vacuum to a higher-energy de Sitter vacuum state. The rate of flyover transitions in this case is parametrically different and can be many orders of magnitude higher than tunneling. This result is in conflict with the conventional picture of quantum de Sitter space as a thermal state. Our numerical simulations indicate that the dynamics of bubble nucleation in flyover transitions is rather different from the standard picture. The difference is especially strong for thin-wall bubbles in flat space, where the transition region oscillates between true and false vacuum until a true vacuum shell is formed which expands both inwards and outwards, and for upward de Sitter transitions, where the inflating new vacuum region is contained inside of a black hole.