Nonlinear growth and amplification of phase-transition gravitational waves induced by cosmic expansion

We perform the first three-dimensional hydrodynamical simulations of cosmological first-order phase transitions in an expanding background. These simulations consistently incorporate the effects of the evolving phase transition strength throughout the full nucleation process of slow phase transitions. We find that, in addition to reducing mean bubble separations via an effectively enhanced nucleation rate, cosmic expansion unexpectedly induces highly nonlinear growth in the gravitational wave energy fraction, ultimately leading to a significant $\mathcal{O}(10)$ to $\mathcal{O}(100)$ amplification of the gravitational wave spectra. This amplification is more pronounced for initially weak transitions than for those of initially intermediate strength. Our results highlight the challenge and importance of accurately modelling slow phase transitions while accounting for cosmic expansion.