Constraining the Gravitational-Wave Spectrum from Cosmological First-Order Phase Transitions Using Data from LIGO-Virgo First Three Observing Runs

Understand

We search for a first-order phase transition (PT) gravitational wave (GW) signal from Advanced LIGO and Advanced Virgo's first three observing runs.

• Due to the large theoretical uncertainties, four GW energy spectral shapes from bubble and sound wave collisions widely adopted in literature are investigated, separately.
• Our results indicate that there is no evidence for the existence of such GW signals, and therefore we give the upper limits on the amplitude of GW energy spectrum $\Omega_\text{pt}(f_*)$ in the peak frequency range of $f_*\in [5,500]$ Hz for these four theoretical models, separately.
• We find that $\Omega_\text{pt}(f_*\simeq 40\ \text{Hz})<1.3\times10^{-8}$ at $95\%$ credible level, and roughly $H_*/\beta\lesssim 0.1$ and $\alpha\lesssim 1$ at $68\%$ credible level in the peak frequency range of $20\lesssim f_*\lesssim 100$ Hz corresponding to the most sensitive frequency band of Advanced LIGO and Advanced Virgo's first three observing runs, where $H_*$ is the Hubble parameter when PT happens, $\beta$ is the bubble nucleation rate and $\alpha$ is the ratio of vacuum and relativistic energy density.