Improving cosmological parameter estimation with the future gravitational-wave standard siren observation from the Einstein Telescope

Detection of gravitational waves produced by the 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.