Improving cosmological parameter estimation with the future
  gravitational-wave standard siren observation from the Einstein Telescope
  Detection of gravitational waves produced by merger of binary compact objects
could provide an independent way for measuring the luminosity distance to the
gravitational-wave burst source, indicating that gravitational-wave
observation, combined with observation of electromagnetic counterparts, can
provide "standard sirens" for investigating the expansion history of the
universe in cosmology. In this work, we wish to investigate how the future
gravitational-wave standard siren observations would break the parameter
degeneracies existing in the conventional optical observations and how they
help improve the parameter estimation in cosmology. We take the
third-generation ground-based gravitational-wave detector, the Einstein
Telescope, as an example to make an analysis. By simulating 1000 events data in
the redshift range between 0 and 5 based on the ten-year observation of the
Einstein Telescope, we find that the gravitational-wave data could largely
break the degeneracy between the matter density and the Hubble constant, thus
significantly improving the cosmological constraints. We further show that the
constraint on the equation-of-state parameter of dark energy could also be
significantly improved by including the gravitational-wave data in the
cosmological fit.
