Detectability of the Phase Transition Gravitational Waves in the DFSZ axion Model

In this work, we investigate the strong first-order phase transition associated with Peccei-Quinn symmetry breaking in the DFSZ axion model. We precisely calculate the phase transition dynamics and the corresponding gravitational wave spectra. It is found that this model allows a strong first-order phase transition over a broad energy scale ranging from $10^{9}~\mathrm{GeV}$ to $10^{12}~\mathrm{GeV}$. Meanwhile, our results are also consistent with current experimental constraints on axions. By comparing these gravitational wave signals with the expected sensitivity curves of Cosmic Explorer and calculating the signal-to-noise ratio, we demonstrate that Cosmic Explorer will be able to detect these signals. We also perform a Fisher matrix analysis to study the sensitivity of gravitational wave detectors to different phase transition parameters. The results show that if signals are observed, the bubble wall velocity will be the first parameter to be determined. This study demonstrates that gravitational wave detection can explore axion physics complementary to other experiments.