Bubble wall correlations in cosmological phase transitions

TL;DR

This paper analyzes the statistical correlations of bubble walls during cosmological first-order phase transitions, focusing on their space-time relationships and implications for the transition's consequences.

Contribution

It introduces a statistical framework for analyzing bubble wall correlations based on nucleation rate and wall velocity, providing general expressions and specific applications.

Findings

Derived expressions for bubble wall correlations in terms of nucleation rate and velocity

Analyzed space-time correlation functions of bubble walls

Discussed implications for cosmological phase transition outcomes

Abstract

We study statistical relationships between bubble walls in cosmological first-order phase transitions. We consider the conditional and joint probabilities for different points on the walls to remain uncollided at given times. We use these results to discuss space and time correlations of bubble walls and their relevance for the consequences of the transition. In our statistical treatment, the kinematics of bubble nucleation and growth is characterized by the nucleation rate and the wall velocity as functions of time. We obtain general expressions in terms of these two quantities, and we consider several specific examples and applications.