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Ultra-low-frequency gravitational waves (GWs) generated by individualinspiraling supermassive black hole binaries (SMBHBs) in the centers ofgalaxies may be detected by pulsar timing arrays (PTAs) in the future. These GWsignals encoding absolute cosmic distances can serve as bright and dark sirens,having potential to be developed into a precise cosmological probe. Here weshow that an SKA-era PTA consisting of 100 millisecond pulsars may observeabout 25 bright sirens and 41 dark sirens during a 10-year observation. Thebright sirens, together with the CMB data, have comparable capabilities tocurrent mainstream data for measuring the equation of state of dark energy. Thedark sirens could make the measurement precision of the Hubble constant closeto that of current distance-ladder observation. Our results indicate thatultra-low-frequency GWs from individual SMBHBs are of great significance inexploring the nature of dark energy and measuring the Hubble constant.

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