Implications for First-Order Cosmological Phase Transitions from the Third LIGO-Virgo Observing Run

We place constraints on the normalized 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, $\Omega_{\rm CBC} < 6.1 \times 10^{-9}$, and strong first-order phase transitions, $\Omega_{\rm BPL} < 4.4 \times 10^{-9}$. The inclusion of the former is necessary since we expect this astrophysical signal to be the foreground of any detected spectrum. 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 phase transitions occurring at temperatures above $10^8$GeV.