Comprehensive analysis of the tidal effect in gravitational waves and implication for cosmology

Detection of gravitational waves (GWs) produced by coalescence of compact binaries provides a novel way to measure the luminosity distance of GW events. Combining their redshift, they can act as standard sirens to constrain cosmological parameters. For various GW detector networks in 2nd-generation (2G), 2.5G and 3G, we comprehensively analyze the method to constrain the equation-of-state (EOS) of binary neutron-stars (BNSs) and extract their redshifts through the imprints of tidal effects in GW waveforms. We find for these events, the observations of electromagnetic counterparts in low-redshift range $z < 0.1$ are important for constraining the tidal effects. Considering 17 different EOSs of NSs or quark-stars, we find GW observations have strong capability to determine the EOS. Applying the events as standard sirens, and considering the constraints of NS's EOS derived from low-redshift observations as prior, we can constrain the dark-energy EOS parameters $w_0$ and $w_a$. In 3G era, the potential constraints are $\Delta w_0\in (0.0006,0.004)$ and $\Delta w_a\in(0.004,0.02)$, which are 1-3 orders smaller than those from traditional methods, including Type Ia supernovas and baryon acoustic oscillations. The constraints are also 1 order smaller than the method of GW standard siren by fixing the redshifts through short-hard $\gamma$-ray bursts, due to more available GW events in this method. Therefore, GW standard sirens, based on the tidal effect measurement, provide a realizable and much more powerful tool in cosmology.