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Supermassive binary black holes (SMBBHs) in galactic centers may radiategravitational wave (GW) in the nano-Hertz frequency band, which are expected tobe detected by pulsar timing arrays (PTAs) in the near future. GW signals fromindividual SMBBHs at cosmic distances, if detected by PTAs, are potentiallypowerful standard sirens that can be used to independently measure distancesand thus put constraints on cosmological parameters. In this paper, weinvestigate 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 inthe Square Kilometre Array (SKA) era. By considering both the currentlyavailable SMBBH candidates and mock SMBBHs in the universe resulting from asimple galaxy major merger model, we find that $\sim 200$ to $3000$ SMBBHs withchirp mass $>10^9M_\odot$ are expected to be detected with signal-to-noiseratio $>10$ by SKA-PTA with conservative and optimistic settings and they canbe used to put a constraint on $w$ to an uncertainty of $\Delta w\sim0.02-0.1$. If further information on the mass and mass ratio of those SMBBHscan 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 betterdistance measurements and can be used as the standard sirens.

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