Cosmic Simulations of Axion String-Wall Networks: Probing Dark Matter and Gravitational Waves for Discovery

We simultaneously study gravitational waves (GWs) and free axions emitted from axionic string-wall networks in the early universe using advanced 3D lattice simulations. Our simulations start before the Peccei-Quinn phase transition and end with the destruction of string-wall networks below the QCD scale. The axion dark matter (DM) relic abundance radiated from string-wall networks are updated and refined for the scenarios of $N_{\rm DW}>1$. In this scenario, we observe that the GW spectrum is almost independent of the bias term and $N_{\rm DW}$, and $\Omega_{\rm GW}h^2\propto f^{1.29}(f^{-0.43})$ in the IR and middle-frequency regions. After considering the constraints from DM relic abundance, we found that the QCD axion model predicts undetectable GW emissions, and the axion-like particles model allows for a detectable GW signal in the nano-Hertz to the milli-Hertz frequency range corresponding to axion masses range from KeV to TeV. For $N_{\rm DW}=1$, the GW energy density appears undetectable for QCD axions and axion-like particles.