Numerical Estimations of the Distribution of the Lifetime of Bubbles Emerging from First Order Cosmological Phase Transitions

TL;DR

This paper develops a numerical framework to estimate the lifetime distribution of bubbles from first order cosmological phase transitions, crucial for predicting gravitational wave signals.

Contribution

It introduces a mathematical approach to better model bubble lifetime distributions, improving predictions of gravitational wave spectra from cosmological phase transitions.

Findings

Good agreement with simulations for detonations

Longer wavelength gravitational waves are more prominent in deflagrations

Highlights need for more accurate bubble lifetime modeling

Abstract

We present a mathematical framework to produce a numerical estimation to the distribution of the lifetime of bubbles emerging from first order cosmological phase transitions. In a precedent work, we have implemented the Sound Shell model to predict the power spectra of gravitational waves arising from the decay of scalar fields. The model depends on the lifetime distribution of bubbles before collision, which in turn depends on the transition rate $\beta$ and the speed of the bubble wall $v$. Empirical exponential laws were used to describe the lifetime distribution and the resultant power spectra. For detonations, the results show a good agreement with simulations where the bubbles have nucleated simultaneously with a mean separation distance. However, for deflagrations, the results show that the amplitude of gravitational waves is higher at longer wavelength than simultaneous nucleation, indicating the importance of having a more accurate description of the lifetime distribution of bubble lifetime.