Axion dark matter from first-order phase transition, and very high energy photons from GRB 221009A

We study an axion-like particle (ALP) that experiences the first-order phase transition with respect to its mass or potential minimum. This can be realized if the ALP obtains a potential from non-perturbative effects of SU($N$) gauge theory that is confined via the first-order phase transition, or if the ALP is trapped in a false vacuum at high temperatures until it starts to oscillate about the true minimum. The resulting ALP abundance is significantly enhanced compared to the standard misalignment mechanism, explaining dark matter in a broader parameter space that is accessible to experiments e.g. IAXO, ALPS-II, and DM-radio. Furthermore, the viable parameter space includes a region of the mass $m_a \simeq 10^{-7} - 10^{-8}$ eV and the ALP-photon coupling $g_{a \gamma \gamma} \simeq 10^{-11} {\rm GeV}^{-1}$ that can explain the recent observation of very high energy photons from GRB221009A via axion-photon oscillations. The parameter region suggests that the FOPT can generate the gravitational wave that explains the NANOGrav hint. If the ALP in this region explains dark matter, then the ALP has likely experienced a first-order phase transition.