Old Phase Remnants in First Order Phase Transitions
  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.
