On using inspiralling supermassive binary black holes in the PTA frequency band as standard sirens to constrain dark energy

Supermassive binary black holes (SMBBHs) in galactic centers may radiate gravitational wave (GW) in the nano-Hertz frequency band, which are expected to be detected by pulsar timing arrays (PTAs) in the near future. GW signals from individual SMBBHs at cosmic distances, if detected by PTAs, are potentially powerful standard sirens that can be used to independently measure distances and thus put constraints on cosmological parameters. In this paper, we investigate the constraint that may be obtained on the equation of state ($w$) of dark energy by using those SMBBHs, expected to be detected by the PTAs in the Square Kilometre Array (SKA) era. By considering both the currently available SMBBH candidates and mock SMBBHs in the universe resulting from a simple galaxy major merger model, we find that $\sim 200$ to $3000$ SMBBHs with chirp mass $>10^9M_\odot$ are expected to be detected with signal-to-noise ratio $>10$ by SKA-PTA with conservative and optimistic settings and they can be used to put a constraint on $w$ to an uncertainty of $\Delta w\sim 0.02-0.1$. If further information on the mass and mass ratio of those SMBBHs can be provided by electromagnetic observations (e.g., chirp mass uncertainty $\lesssim 50\%$), the constraint may be further improved to $\lesssim 0.01$ level, as many more SMBBHs will be detected by SKA-PTA with relatively better distance measurements and can be used as the standard sirens.