Gravitational Waves from First-Order Phase Transition in a Simple Axion-Like Particle Model

We consider a gauge-singlet complex scalar field $\Phi$ with a global $U(1)$ symmetry that is spontaneously broken at some high energy scale $f_a$. As a result, the angular part of the $\Phi$-field becomes an axion-like particle (ALP). We show that if the $\Phi$-field has a non-zero coupling $\kappa$ to the Standard Model Higgs boson, there exists a certain region in the $\left(f_a, \kappa\right)$ parameter space where the global $U(1)$ symmetry-breaking induces a strongly first order phase transition, thereby producing stochastic gravitational waves that are potentially observable in current and future gravitational-wave detectors. In particular, we find that future gravitational-wave experiments such as TianQin, BBO and Cosmic Explorer could probe a broad range of the energy scale $10^3 \, {\rm GeV} \lesssim f_a \lesssim 10^{8} \, {\rm GeV}$, independent of the ALP mass. Since all the ALP couplings to the Standard Model particles are proportional to inverse powers of the energy scale $f_a$ (up to model-dependent ${\cal O}(1)$ coefficients), the gravitational-wave detection prospects are largely complementary to the current laboratory, astrophysical and cosmological probes of the ALP scenarios.