Numerical simulations of density perturbation and gravitational wave production from cosmological first-order phase transition

TL;DR

This study uses 3D lattice simulations to analyze density perturbations and gravitational waves from first-order phase transitions, revealing how transition strength affects bubble dynamics and perturbation spectra.

Contribution

The paper presents new numerical results on the impact of phase transition strength on density perturbations and gravitational wave spectra during cosmological FOPTs.

Findings

Bubble wall motion dominates for $oldsymbol{ ext{alpha} > 1}$.

Density perturbation spectrum has a $k^3$ slope at small $k$ and $k^{-1.5}$ at large $k$.

GW spectrum shows a $k^3$ slope at small $k$ and $k^{-2}$ at large $k$.

Abstract

We conducted three-dimensional lattice simulations to study the density perturbation and gravitational waves (GWs) during first-order phase transition (FOPT). We find that for phase transition strength $\alpha > 1$, the forward motion of bubble walls becomes the primary source, whereas for $\alpha < 1$, the dominant contribution to the density perturbation comes from the delay of vacuum decay. Additionally, the power spectrum of density perturbations generated by the phase transition exhibits a slope of $k^3$ at small wavenumbers and $k^{-1.5}$ at large wavenumbers. Furthermore, we calculated the GW power spectra, which exhibit the slope of $k^3$ at small wavenumbers and $k^{-2}$ at large wavenumbers. Our numerical simulations confirm that slow PTs can produce PBHs and provide predictions for the GW power spectrum, offering theoretical support for GW detection.