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

TL;DR

The paper develops a hierarchical Bayesian framework to jointly infer the neutron star EoS, population properties (mass and redshift), and cosmology from dark BNS gravitational-wave signals. By incorporating tidal deformability via the $m$–$\Lambda$ relation and marginalizing over population and selection effects, the method constrains the Hubble constant $H_{0}$ and the maximum NS mass $m_{\max}$ even without EM counterparts, achieving $\lesssim 35\%$ precision for $H_{0}$ with 50 simulated O5-era events. The inclusion of EoS information tightens correlations and improves parameter estimates, though $\Omega_{m}$ remains weakly constrained at low redshift; the results depend on the assumed NS mass distribution (Gaussian vs double Gaussian). The approach is scalable to future detectors and can be augmented with laboratory priors on EoS parameters and additional multi-messenger data, offering a path to EM-free cosmology and nuclear-physics inference from gravitational waves.

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 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 $\lesssim 35\%$ ($90\%$ 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 $5$ simulated BNS events.

Figures (14)

• Figure 1: Top Row: The left and right panels show the injected and detected component mass distributions of NSs for the Gaussian and double Gaussian mass models, respectively. The black solid lines indicate the true mass distributions (see Table \ref{['tab:mass_model_parameters']}), and histograms correspond to the source-frame masses of $5$ and $50$ NSs detected with SNR $\geq 20$. Bottom Row: The left and right panels display the luminosity distance distributions of the detected events for the same mass models. The black lines represent the underlying true distributions, while the histograms show results for $5$ and $50$ detected NSs with SNR $\geq 20$.
• Figure 2: Comparison of the inferred population and cosmological parameters from $5$ events, based on the Gaussian mass distribution, detected by the LIGO-Virgo detectors. The label 'Population' refers to the Bayesian analysis considering only mass and redshift information ($m_{1}, m_{2}, z$), while the other label 'EoS+Population' also includes tidal parameters ($m_{1}, m_{2}, z, \Lambda_{1}, \Lambda_{2}$). The black solid lines indicate the injected values of the corresponding parameters. The $90\%$ credible intervals are shown for each of the respective marginalized $1$D posteriors.
• Figure 3: Same as Fig. \ref{['fig:pop_parameters_compare_5events_gaussian']}, but using $50$ events.
• Figure 4: Comparison of the inferred population and cosmological parameters from $5$ GW events, following the double Gaussian mass distribution, detected by the LIGO-Virgo detectors. The black solid lines show the injected values of the corresponding parameters. The $90\%$ credible intervals are also mentioned for each of the respective marginalized $1$D posteriors.
• Figure 5: Same as Fig. \ref{['fig:pop_parameters_compare_5events_double_gaussian']}, but using $50$ events.