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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., Comment: References updated, 37 pages, 4 figures, 5 tables, comments are welcome

For the first time, the expected stochastic gravitational wave background is probably discovered after observing the Hellings Downs correlation curve by several pulsar timing array (PTA) collaborations around the globe including NANOGrav, European PTA, Parkes PTA, and Chinese PTA. These new observations can help to explore or constrain the dark matter (DM) formation mechanisms in the early Universe. We study the implication of those results on the dynamical DM formation mechanisms through a dark first-order phase transition in the early Universe. Both the Q-ball DM and super-cool DM are investigated in the strong super-cooling dark phase transition scenario which may give an interpretation of the observed stochastic gravitational wave background., Comment: Published version at Classical and Quantum Gravity, 27 pages, 6 figures, 2 tables