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

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology