High-Quality Axion Dark Matter at Gravitational Wave Interferometers

Gravitational effects are known to violate global symmetries, threatening the Peccei-Quinn (PQ) solution to the strong CP problem. Ultraviolet completions featuring a gauged $U(1)$ symmetry, where $U(1)_{\rm PQ}$ arises as an accidental global symmetry, can suppress Planck-suppressed operators, enabling high-quality axions in a mass window where it can also account for the observed dark matter (DM) in the Universe. We show that in such models, the spontaneous breaking of the $U(1)$ gauge symmetry generates a strong stochastic gravitational wave background (SGWB) from gauge cosmic string loops. Even in the most conservative scenario, for breaking scales $\gtrsim 10^{14}$ GeV, the SGWB signal strength can exceed astrophysical foregrounds across a broad frequency range. Such quality axion models have a characteristic IR break frequency originating from the dynamics of the string-wall network collapse. We propose this characteristic SGWB frequency-amplitude region, identified as \textit{Signature-Window-Axion-Gravitational waves} (SWAG), to be a novel probe of high-quality axion DM at future space and ground-based interferometers.