Implications for first-order cosmological phase transitions from the third LIGO-Virgo observing run.

We place constrains on the normalised energy density in gravitational waves from first-order strong phase transitions using data from Advanced LIGO and Virgo's first, second and third observing runs. First, adopting a broken power law model, we place $95 \%$ confidence level upper limits simultaneously on the gravitational-wave energy density at 25 Hz from unresolved compact binary mergers, $\Omega_{\rm cbc} < 5.9 \times 10^{-9}$, and strong first-order phase transitions, $\Omega_{\rm bpl} < 2.8 \times 10^{-9}$. We then consider two more complex phenomenological models, limiting at 25 Hz the gravitational-wave background due to bubble collisions to $\Omega_{\rm pt} < 5.0\times 10^{-9}$ and the background due to sound waves to $\Omega_{\rm pt} < 5.8\times10^{-9}$ at $95 \%$ confidence level for temperatures above $10^8$GeV.