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

Figure 1

Posterior distributions for the combined CBC and broken power law search as a function of $\log {\mathrm{\Omega }}_{\mathrm{ref}}$ and the different parameters of the model. The 68% and 95% CL exclusion contours are shown. The horizontal dashed line in the posteriors indicate the flat priors used in the analysis.

Figure 2

Posterior distributions for the $\mathrm{CBC}+\mathrm{FOPT}$ search in the case of a phenomenological model with dominant bubble collision contributions as a function of $\log {\mathrm{\Omega }}_{\mathrm{ref}}$ and the different parameters of the model. The 68% and 95% CL exclusion contours are shown. The horizontal dashed lines in the posteriors indicate the flat priors used in the analysis.

Figure 3

Posterior distributions for the $\mathrm{CBC}+\mathrm{FOPT}$ search in the case of a phenomenological model with dominant sound wave contributions ($v_w=1$), as a function of $\log {\mathrm{\Omega }}_{\mathrm{ref}}$ and the different parameters of the model. The 68% and 95% CL exclusion contours are shown. The horizontal dashed lines in the posteriors indicate the flat priors used in the analysis.