Estimating cosmological parameters by the simulated data of
  gravitational waves from the Einstein Telescope
  We investigate the constraint ability of the gravitational wave (GW) as the
standard siren on the cosmological parameters by using the third-generation
gravitational wave detector: the Einstein Telescope. We simulate the luminosity
distances and redshift measurements from 100 to 1000 GW events. We use two
different algorithms to constrain the cosmological parameters. For the Hubble
constant $H_0$ and dark matter density parameter $\Omega_m$, we adopt the
Markov chain Monte Carlo approach. We find that with about 500-600 GW events we
can constrain the Hubble constant with an accuracy comparable to
\textit{Planck} temperature data and \textit{Planck} lensing combined results,
while for the dark matter density, GWs alone seem not able to provide the
constraints as good as for the Hubble constant; the sensitivity of 1000 GW
events is a little lower than that of \textit{Planck} data. It should require
more than 1000 events to match the \textit{Planck} sensitivity. Yet, for
analyzing the more complex dynamical property of dark energy, i.e., the
equation of state $w$, we adopt a new powerful nonparametric method: the
Gaussian process. We can reconstruct $w$ directly from the observational
luminosity distance at every redshift. In the low redshift region, we find that
about 700 GW events can give the constraints of $w(z)$ comparable to the
constraints of a constant $w$ by \textit{Planck} data with type Ia supernovae.
Those results show that GWs as the standard sirens to probe the cosmological
parameters can provide an independent and complementary alternative to current
experiments.
