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. The binary merger of a neutron with either a neutron or black hole is hypothesized to be the progenitor of a short and intense burst of γ rays, some fraction of those binary mergers could be detected both through electromagnetic radiation and gravitational waves. Thus we can determine both the luminosity distance and redshift of the source separately. 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 H0 and dark matter density parameter Ωm, 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 Planck temperature data and 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 Planck data. It should require more than 1000 events to match the 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 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.

The direct detection of gravitational wave by Laser Interferometer Gravitational-Wave Observatory indicates the coming of the era of gravitational-wave astronomy and gravitational-wave cosmology. It is expected that more and more gravitational-wave events will be detected by currently existing and planned gravitational-wave detectors. The gravitational waves open a new window to explore the Universe and various mysteries will be disclosed through the gravitational-wave detection, combined with other cosmological probes. The gravitational-wave physics is not only related to gravitation theory, but also is closely tied to fundamental physics, cosmology and astrophysics. In this review article, three kinds of sources of gravitational waves and relevant physics will be discussed, namely gravitational waves produced during the inflation and preheating phases of the Universe, the gravitational waves produced during the first-order phase transition as the Universe cools down and the gravitational waves from the three phases: inspiral, merger and ringdown of a compact binary system, respectively. We will also discuss the gravitational waves as a standard siren to explore the evolution of the Universe.