Nucleation of vacuum bubbles in Brans-Dicke type theory

TL;DR

This paper investigates the nucleation of vacuum bubbles in Brans-Dicke gravity, analyzing different scenarios for true and false vacuum bubbles and their evolution, highlighting the conditions under which they form.

Contribution

It provides a detailed analysis of vacuum bubble nucleation in Brans-Dicke type theories, including multiple scenarios and the continuation of bubble evolution from Euclidean to Lorentzian signatures.

Findings

Vacuum bubbles can be true or false depending on ta>-3/2 or ta<-3/2.

Bubble nucleation probabilities are computed via Euclidean action.

Vacuum bubble evolution can be smoothly continued from Euclidean to Lorentzian signature.

Abstract

In this paper, we explore the nucleation of vacuum bubbles in the Brans-Dicke type theory of gravity. In the Euclidean signature, we evaluate the fields at the vacuum bubbles as solutions of the Euler-Lagrange equations of motion as well as the bubble nucleation probabilities by integrating the Euclidean action. We illustrate three possible ways to obtain vacuum bubbles: true vacuum bubbles for \omega>-3/2, false vacuum bubbles for \omega<-3/2, and false vacuum bubbles for \omega>-3/2 when the vacuum energy of the false vacuum in the potential of the Einstein frame is less than that of the true vacuum. After the bubble is nucleated at the t=0 surface, we can smoothly interpolate the field combinations to some solutions in the Lorentzian signature and consistently continue their subsequent evolutions. Therefore, we conclude that, in general scalar-tensor theories like this Brans-Dicke type theories, which may include and represent certain features of string theory, vacuum bubbles come in false vacuum bubbles as well as in true vacuum bubbles, as long as a special condition is assumed on the potential.