Gravitational waves from cosmic strings associated with pseudo-Nambu-Goldstone dark matter

We study stochastic gravitational waves from cosmic strings generated in an ultraviolet-complete model for pseudo-Nambu-Goldstone dark matter with a hidden $\mathrm{U(1)}$ gauge symmetry. The dark matter candidate in this model can naturally evade direct detection bounds and easily satisfy other phenomenological constraints. The bound on the dark matter lifetime implies an ultraviolet scale higher than $10^9~\mathrm{GeV}$. The spontaneous $\mathrm{U(1)}$ symmetry breaking at such a high scale would induce cosmic strings with high tension, resulting in a stochastic gravitational wave background with a high energy density. We investigate the constraints from current gravitational wave experiments as well as the future sensitivity. We find that most viable parameter points can be well studied in future gravitational wave experiments.