Achieving precision cosmology with gravitational-wave bright sirens from
  SKA-era pulsar timing arrays
  Nanohertz gravitational waves (GWs) generated by the individual inspiraling
supermassive black hole binaries (SMBHBs) in the centers of galaxies may be
detected by pulsar timing arrays (PTAs) in the future. The GW signals from
individual SMBHBs can be employed as standard sirens to measure absolute cosmic
distances, and further provide constraints on cosmological parameters via the
distance--redshift relation. Namely, these SMBHBs with known redshifts can
serve as bright sirens. In this paper, we analyze the ability of SKA-era PTAs
to detect existing SMBHB candidates by means of simulating the timing residuals
of pulsar signals, and use the mock data of SMBHB bright sirens to perform
cosmological parameter estimations. We find that once the root mean square of
timing residuals ($\sigma_t$) could be reduced to 20 ns, about only 100
millisecond pulsars are needed to provide a tight constraint on the Hubble
constant ($H_0$) with the precision close to $1\%$, which meets the criterion
of precision cosmology. We further show that the SMBHB bright sirens can
effectively break the cosmological parameter degeneracies inherent in the CMB
data, and thus improve the constraint precision of the equation of state of
dark energy ($w$) to $3.5\%$, which is comparable with the result of Planck
2018 TT,TE,EE+lowE+lensing+SNe+BAO. We conclude that the bright sirens from
SKA-era PTAs will play an important role in breaking the cosmological parameter
degeneracies and exploring the nature of dark energy.
