Gravitational wave and dark matter from Axion-Higgs string

Axions have long been considered plausible candidates for dark matter. The axion dark matter emitted from cosmic strings after the Peccei-Quinn (PQ) symmetry breaking in the early Universe was extensively simulated. In this work, we study dark matter and gravitational waves through the lattice simulation of the Axion-Higgs string. We gave the dark matter overproduction and the Big Bang nucleosynthesis bounds on the axion decay constant $f_a$ and the axion mass $m_a$ for axion-like particles, and found that the predicted gravitational wave spectra cannot be probed by the dataset of the current pulsar timing array experiments.