Stochastic tunneling in de Sitter spacetime

TL;DR

This paper applies the stochastic approach using the MSRJD functional integral to analyze tunneling processes in de Sitter spacetime, reproducing known rates and exploring bubble nucleation with potential applications in inflationary cosmology.

Contribution

It introduces a novel stochastic method for studying tunneling in de Sitter space, clarifies its applicability, and connects it with established formalisms like Schwinger-Keldysh.

Findings

Reproduces Hawking-Moss tunneling rate for shallow barriers.

Derives physically natural boundary conditions for tunneling configurations.

Identifies bubble-like solutions for steep potential barriers.

Abstract

Tunneling processes in de Sitter spacetime are studied by using the stochastic approach. We exploit the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional integral to obtain the tunneling rate. The applicability conditions of this method are clarified using the Schwinger-Keldysh formalism. In the case of a shallow potential barrier, we reproduce the Hawking-Moss (HM) tunneling rate. Remarkably, in contrast to HM picture, the configuration derived from the MSRJD functional integral satisfies physically natural boundary conditions. We also discuss the case of a steep potential barrier and find an interesting Coleman-de Luccia (CDL) bubble-like configuration. Our results demonstrate how the bubble nucleation process could be described in the stochastic approach. Our method turns out to be useful for investigating various tunneling processes during inflation.