Ultra-low-frequency gravitational waves from individual supermassive black hole binaries as standard sirens

Ultra-low-frequency gravitational waves (GWs) generated by individual inspiraling supermassive black hole binaries (SMBHBs) at the centers of galaxies may be detected by pulsar timing arrays (PTAs) in the future. These GW signals, which encode absolute cosmic distances, can serve as bright and dark sirens, potentially evolving into a precise cosmological probe. Here, we show that a PTA in the era of the Square Kilometre Array, comprising 100 millisecond pulsars, could potentially detect about 25 bright sirens and 41 dark sirens over a 10-year observation period. The bright sirens, combined with cosmic microwave background data, offer capabilities comparable to current mainstream joint cosmological observations for measuring the equation of state of dark energy. The dark sirens could achieve a measurement precision of the Hubble constant close to that of current distance-ladder observations. Our results suggest that ultra-low-frequency GWs from individual SMBHBs are of great significance in investigating the nature of dark energy and determining the Hubble constant.