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 $10\sim 200$ Hz, and get the most stringent limitation at the peak frequency $f_{\ast }=35$ Hz, namely ${\mathrm{\Omega }}_{\text{DW}}(f_{\ast }=35\text{Hz})<1.4\times {10}^{-8}$ at $95\mathrm{\%}$ 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.