We investigate the gravitational waves (GWs) produced from the Peccei-Quinn (PQ) phase transition associated with the clockwork axion. The PQ phase transition can be first-order when the dimension-6 operator is included into the scalar potential. The GWs from the PQ phase transition at scale in the range of 10³-10⁶ GeV are detectable for the BBO and ALIA interferometers. The LISA and Taiji interferometers can probe the GWs from the PQ scale f ≤ 10⁴ GeV, while the GW signals from the scale f ≥ 10⁵ GeV can be detected by the ground-based GW observatories ET and CE. We find that the parameter space κ_m ∼ 0.06-0.001, κ_l ∼ 0.04-0.001, and ε ∼ 0.1-0.01 at the scale f = 10⁵ GeV and most of the parameter regions at the scale f = 10⁶ GeV have been excluded by the LIGO O2 run. The LIGO O3 and design phases can further probe the remaining parameter space. We show that the GWs from the annihilation of domain walls with a PQ scale f ≃ 2 10⁵ GeV can induce the stochastic signals with the right amplitude for the NANOGrav 12.5-year observations, but having a steeper spectral slope than the observations. The LIGO O3 run has the opportunity of detecting the GW signals from the first-order PQ phase transition around this scale.

我们研究了与发条轴子相关的 Peccei-Quinn (PQ) 相变产生的引力波 (GW)。当 6 维算子包含在标量势中时，PQ 相变可以是一阶的。对于 BBO 和 ALIA 干涉仪，可在10 ³ -10 ⁶ GeV范围内检测到来自 PQ 相变的 GW 。LISA和太极干涉仪可以探测PQ尺度f≤10 4 GeV^的GW，而地面GW天文台ET和CE可以探测到f≥10 5 GeV尺度^的GW信号。我们发现参数空间κ _m ∼ 0.06-0.001, κ _l ～ 0.04-0.001 和 ε ～ 0.1-0.01 在尺度f = 10 ^{5 GeV 和尺度}f = 10 ⁶ GeV的大部分参数区域已被 LIGO O2 运行排除。LIGO O3 和设计阶段可以进一步探索剩余的参数空间。我们表明，具有 PQ 尺度f ≃ 2 10 ⁵ GeV 的畴壁湮灭产生的 GW 可以在 NANOGrav 12.5 年的观测中诱导出具有正确幅度的随机信号，但具有比观测更陡的光谱斜率。LIGO O3 运行有机会检测来自该尺度的一阶 PQ 相变的 GW 信号。