Coleman-de Luccia Tunneling and the Gibbons-Hawking Temperature

TL;DR

This paper analyzes various types of Coleman-de Luccia tunneling in de Sitter space, highlighting the role of thermal fluctuations and quantum effects, and discusses implications for the cosmic landscape.

Contribution

It classifies four tunneling types depending on potential properties and estimates corrections to Hawking-Moss tunneling, linking tunneling behavior to the Gibbons-Hawking temperature.

Findings

Tunneling decreases rapidly with increasing vacuum energy density.

Thermal fluctuations significantly influence tunneling processes.

Corrections to Hawking-Moss tunneling can be large.

Abstract

We study Coleman-de Luccia tunneling in some detail. We show that, for a single scalar field potential with a true and a false vacuum, there are four types of tunneling, depending on the properties of the potential. A general tunneling process involves a combination of thermal (Gibbons-Hawking temperature) fluctuation part way up the barrier followed by quantum tunneling. The thin-wall approximation is a special limit of the case (of only quantum tunneling) where inside the nucleation bubble is the true vacuum while the outside reaches the false vacuum. Hawking-Moss tunneling is the (only thermal fluctuation) limit of the case where the inside of the bubble does not reach the true vacuum at the moment of its creation, and the outside is cut off by the de Sitter horizon before it reaches the false vacuum. We estimate the corrections to the Hawking-Moss formula, which can be large. In all cases, we see that the bounce of the Euclidean action decreases rapidly as the vacuum energy density increases, signaling that the tunneling is not exponentially suppressed. In some sense, this phenomenon may be interpreted as a finite temperature effect due to the Gibbons-Hawking temperature of the de Sitter space. As an application, we discuss the implication of this tunneling property to the cosmic landscape.