Joint Inference of Population, Cosmology, and Neutron Star Equation of State from Gravitational Waves of Dark Binary Neutron Stars

Abstract Gravitational waves (GWs) from binary neutron stars (BNSs) are expected to be accompanied by electromagnetic (EM) emissions, which help identify the host galaxy. Since GWs directly measure their luminosity distances, joint GW–EM observations from BNSs help with the study of cosmology, particularly the Hubble constant, unaffected by cosmic distance ladder systematics. However, detecting the EM emissions is not always possible. Additionally, the tidal deformability of neutron stars (NSs), combined with the knowledge of the NS equation of state (EoS), can break the degeneracy between mass parameters and redshift, allowing for the inference of the Hubble constant. While several studies have aimed to infer the Hubble constant using dark BNSs (without EM counterparts), none have consistently combined the uncertainties of population, cosmology, and NS EoS within a Bayesian framework. In this study, we propose a novel Bayesian analysis to jointly constrain the NS EoS, population, and cosmological parameters using a population of dark BNSs detected through GW observations. We demonstrate the statistical robustness of our method using 50 simulated BNS events following Gaussian and double Gaussian mass distributions, detected by Advanced LIGO and Advanced Virgo detectors operating at O5 sensitivity. We show that such measurements can constrain the Hubble constant with a precision of ≲35% (90% credible interval). This level of precision is unattainable without incorporating NS EoS, especially when observing BNS mergers without EM counterpart information. We also report the Hubble constant measurements obtained from a more realistic set of five simulated BNS events.