The constraint ability of Hubble parameter by gravitational wave
  standard sirens on cosmological parameters
  In this paper, we present the application of a new method measuring Hubble
parameter $H(z)$ by using the anisotropy of luminosity distance($d_{L}$) of the
gravitational wave(GW) standard sirens of neutron star(NS) binary system. The
method has never been put into practice so far due to the lack of the ability
of detecting GW. However, LIGO's success in detecting GW of black hole(BH)
binary system merger announced the potential possibility of this new method. We
apply this method to several GW detecting projects, including Advanced
LIGO(aLIGO), Einstein Telescope(ET) and DECIGO, and evaluate its constraint
ability on cosmological parameters of $H(z)$. It turns out that the $H(z)$ by
aLIGO and ET is of bad accuracy, while the $H(z)$ by DECIGO shows a good one.
We simulate $H(z)$ data at every 0.1 redshift span using the error information
of $H(z)$ by DECIGO, and put the mock data into the forecasting of cosmological
parameters. Compared with the previous data and method, we get an obviously
tighter constraint on cosmological parameters by mock data, and a concomitantly
higher value of Figure of Merit(FoM, the reciprocal of the area enclosed by the
$2\sigma$ confidence region). For a 3-year-observation by standard sirens of
DECIGO, the FoM value is as high as 170.82. If a 10-year-observation is
launched, the FoM could reach 569.42. For comparison, the FoM of 38 actual
observed $H(z)$ data(OHD) is 9.3. We also investigate the undulant universe,
which shows a comparable improvement on the constraint of cosmological
parameters. These improvement indicates that the new method has great potential
in further cosmological constraints.
