Implications for Cosmic Domain Walls from LIGO-Virgo First Three Observing Runs

We put constraints on the normalized energy density in gravitaional waves from cosmic domain walls (DWs) by searching for the stochastic gravitational-wave background (SGWB) in the data of Advanced LIGO and Virgo's first three observing runs. By adopting a phenomenological broken power-law model, we obtain the upper limit of normalized energy density of SGWB generated by DWs in the peak frequency band $10\sim200$ Hz, and get the most stringent limitation at the peak frequency $f_*=35$ Hz, namely $\Omega_\text{DW}(f_*=35\,\text{Hz})<1.4\times10^{-8}$ at $95\%$ confidence level (CL). Subsequently, we work out the constraints on the parameter space in the appealing realization of DW structure -- the heavy axion model which can avoid the so-called quality problem.
Comment: 7 pages, 2 tables and 4 figures