Building a Better Beta: Nucleation and Timescales in Cosmological Phase Transitions

Abstract

First-order phase transitions in the early universe can generate a stochastic background of gravitational waves, offering a unique probe of high-energy physics. In this work, we investigate aspects of bubble nucleation and transition timescales, which play a central role in shaping the resulting gravitational wave spectrum. Many common approaches characterise the transition rate via a Taylor expansion of the false vacuum decay rate. We argue that a more fundamental description is instead given by the distribution of bubble lifetimes, and define a new timescale, $\beta_\nu$, as the first moment of this distribution. We show that $\beta_\nu$ reproduces the behaviour of previous timescale definitions in the appropriate limits, while avoiding their pathologies, and offers a more natural description of the ensemble of nucleated bubbles. We then quantify the impact of this improved timescale on the predicted gravitational wave spectrum, finding that it shifts the peak amplitude by up to an order of magnitude relative to previous definitions. As next-generation gravitational wave detectors come online, robust theoretical predictions will be essential; we hope this work represents a step in that direction.