Multimessenger Detection Rates and Distributions of Binary Neutron Star Mergers and Their Cosmological Implications

Gravitational wave (GW) events, produced by the coalescence of binary neutron stars (BNSs), can be treated as the standard sirens to probe the expansion history of the universe, if their redshifts can be determined from electromagnetic (EM) observations. For the high-redshift (z ≳ 0.1) events, the short γ-ray bursts (sGRBs) and the afterglows are always considered as the primary EM counterparts. In this paper, by investigating various models of sGRBs and afterglows, we discuss the rates and distributions of the multimessenger observations of BNS mergers using GW detectors in the second-generation (2G), 2.5G, and 3G era with detectable sGRBs and afterglows. For instance, for the Cosmic Explorer GW detector, the rate is about 300-3500 yr^-1 with a GECAM-like detector for γ-ray emissions and an LSST/WFST detector for optical afterglows. In addition, we find that these events have redshifts z ≲ 2 and inclination angles ι ≲ 20°. These results justify the rough estimation in previous works. Considering these events as standard sirens to constrain the equation-of-state parameters of dark energy w₀ and w_a, we obtain the potential constraints of Δw₀ ≃ 0.02-0.05 and Δw_a ≃ 0.1-0.4.