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 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) GeV less than or similar to f(a) less than or similar to 10(8) 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 O (1) coefficients), the gravitational-wave detection prospects are largely complementary to the current laboratory, astrophysical and cosmological probes of the ALP scenarios.