  As a promising dark matter candidate, the axion particle can naturally solve
the strong CP problem of the Standard Model through the U(1) Peccei-Quinn
symmetry breaking process. However, detecting this high-energy process poses a
significant challenge for colliders. We precisely calculate phase transition
gravitational wave signals of this symmetry breaking process in the popular
DFSZ axion model. By comparing these signals with the expected sensitivity
curves of the Cosmic Explorer and the Einstein Telescope, we demonstrate that
Cosmic Explorer can detect this process with a signal-to-noise ratio higher
than 8 for the benchmark points. Furthermore, by performing a Fisher analysis,
we find that if signals are observed, the bubble wall velocity will be the
first phase transition parameter to be determined. Future gravitational wave
detectors are expected to provide a new approach for exploring concrete axion
models.
