[Paper Review] Cosmology with Love: Measuring the Hubble constant using neutron star universal relations

Deep Chatterjee, Abhishek Hegade K. R.+5 more|arXiv (Cornell University)|Jun 11, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy66 references50 citations

TL;DR

This paper proposes a novel method to measure the Hubble constant (H₀) using gravitational waves from binary neutron star mergers without requiring electromagnetic counterparts. By leveraging EoS-insensitive binary Love relations to break the mass-redshift degeneracy in gravitational-wave data, the approach enables direct redshift inference and H₀ estimation. The method achieves ~10% accuracy with O(10²) events in the LIGO Voyager era and ~2% accuracy with O(10³) events in the Cosmic Explorer era, offering a promising dark-siren alternative to standard siren cosmology.

ABSTRACT

Gravitational-wave cosmology began in 2017 with the observation of the gravitational waves emitted in the merger of two neutron stars, and the coincident observation of the electromagnetic emission that followed. Although only a $30\%$ measurement of the Hubble constant was achieved, future observations may yield more precise measurements either through other coincident events or through cross correlation of gravitational-wave events with galaxy catalogs. Here, we implement a new way to measure the Hubble constant without an electromagnetic counterpart and through the use of the binary Love relations. These relations govern the tidal deformabilities of neutron stars in an equation-of-state insensitive way. Importantly, the Love relations depend on the component masses of the binary in the source frame. Since the gravitational-wave phase and amplitude depend on the chirp mass in the observer (and hence redshifted) frame, one can in principle combine the binary Love relations with the gravitational-wave data to directly measure the redshift, and thereby infer the value of the Hubble constant. We implement this approach in both real and synthetic data through a Bayesian parameter estimation study in a range of observing scenarios. We find that for the LIGO/Virgo/KAGRA design sensitivity era, this method results in a similar measurement accuracy of the Hubble constant to those of current-day, dark-siren measurements. For third generation detectors, this accuracy improves to $\lesssim 10\%$ when combining measurements from binary neutron star events in the LIGO Voyager era, and to $\lesssim 2\%$ in the Cosmic Explorer era.

Motivation & Objective

• To develop a cosmological distance-redshift measurement technique using gravitational waves from binary neutron star mergers without electromagnetic counterparts.
• To overcome the mass-redshift degeneracy in standard siren cosmology by exploiting EoS-insensitive universal relations between tidal deformability expansion coefficients.
• To enable H₀ estimation using only gravitational-wave data by fixing the universal coefficient ¯λ(0)₀ from prior observations and stacking multiple events.
• To assess the precision and systematic uncertainties of this method across different detector sensitivity eras, from LIGO/Virgo/KAGRA to Cosmic Explorer.

Proposed method

• The method uses the universal binary Love relations (YY17) to relate tidal deformability expansion coefficients ¯λ(0)₀ and ¯λ(k)₀, which are insensitive to the neutron star equation of state.
• The coefficient ¯λ(0)₀ is measured via Bayesian parameter estimation on GW170817 data using a relation constructed from EoSs consistent with LIGO/Virgo and NICER constraints.
• For future events, the fixed ¯λ(0)₀ value is used to infer source-frame masses from gravitational-wave phasing, breaking the redshift-mass degeneracy and enabling redshift and H₀ estimation.
• The approach combines data from multiple simulated binary neutron star events across different detector sensitivity eras (HLVKI, Voyager, Cosmic Explorer) to improve statistical precision.
• Bayesian inference is used throughout to estimate posterior distributions of H₀, incorporating uncertainties in the universal relations and measurement of ¯λ(0)₀.
• Systematic uncertainties from imperfect knowledge of the ¯λ(0)₀−¯λ(k)₀ relation and ¯λ(0)₀ measurement are quantified to assess their impact on final H₀ accuracy.

Experimental results

Research questions

• RQ1 Can the Hubble constant be measured from gravitational waves alone using universal relations, without electromagnetic counterparts?
• RQ2 How precisely can H₀ be estimated using the binary Love relations across different generations of gravitational-wave detectors?
• RQ3 What is the impact of systematic uncertainties in the universal relations and ¯λ(0)₀ measurement on H₀ inference?
• RQ4 How many binary neutron star events are needed to achieve sub-10% H₀ precision in future detector networks?
• RQ5 Can stacking multiple dark-siren events yield a convergent measurement of H₀ that matches the true value?

Key findings

• For the LIGO/Virgo/KAGRA/India design sensitivity era, the method achieves H₀ measurement accuracy comparable to current dark-siren measurements, with a precision of approximately 10%.
• In the LIGO Voyager era, combining O(10²) binary neutron star events reduces H₀ uncertainty to ∼10%.
• In the Cosmic Explorer era, stacking O(10³) events enables H₀ measurement with a precision of ∼2%.
• The method's accuracy is limited by systematic uncertainties in the universal relations and the measurement of ¯λ(0)₀, which must be controlled to achieve sub-2% precision.
• The Bayesian parameter estimation framework successfully recovers the true H₀ value through stacking, demonstrating convergence of the method across multiple events.
• The approach provides a viable alternative to standard siren cosmology by eliminating the need for electromagnetic counterparts, enhancing robustness in H₀ measurements.