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 second-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 that the observations of electromagnetic counterparts in the 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 w0 and wa. In the 3G era, the potential constraints are Δw0 (0.0006,0.004) and Δwa (0.004,0.02), which are 1-3 orders smaller than those from traditional methods, including Type Ia supernovae (SNe Ia) and baryon acoustic oscillations. The constraints are also made 1 order smaller than the method of GW standard siren by fixing the redshifts through short-hard γ-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.