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, Ω_{CBC}<6.1×10^{-9}, and strong first-order phase transitions, Ω_{BPL}<4.4×10^{-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 Ω_{pt}<5.0×10^{-9} and the background due to sound waves to Ω_{pt}<5.8×10^{-9} at 95% confidence level for phase transitions occurring at temperatures above 10^{8} GeV.