Old Phase Remnants in First Order Phase Transitions

TL;DR

This paper introduces a new formalism for analyzing the remnants of old phase regions in first order phase transitions, providing analytical tools to understand their distribution and evolution, with implications for cosmology and other fields.

Contribution

It develops the first analytical framework for the statistics of shrinking old phase remnants in FOPTs, linking them to expanding bubbles via reverse time analysis.

Findings

Derived analytical distribution of old phase remnants.

Established the connection between shrinking remnants and expanding bubbles.

Provided quantitative evolution models for remnants in FOPTs.

Abstract

First order phase transitions (FOPTs) are usually described by the nucleation and expansion of new phase bubbles in the old phase background. While the dynamics of new phase bubbles have been extensively studied, a comprehensive treatment of the shrinking old phase remnants remained undeveloped. We present a novel formalism for remnant statistics in FOPTs and perform the first analytical calculations of their distribution. By shifting to the reverse time description, we identify the shrinking remnants with expanding old phase bubbles, allowing a quantitative evolution and determination of the population statistics. Our results not only provide essential input for cosmological FOPT-induced soliton/primordial black hole formation scenarios, but can also be readily applied to generic FOPTs.