[Paper Review] Using Gray Sirens to Resolve the Hubble-Lemaître Tension

Ish Gupta|arXiv (Cornell University)|Nov 30, 2022

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper proposes neutron star-black hole (NSBH) mergers—termed 'gray sirens'—as a dual-capability tool for measuring the Hubble-Lemaître constant ($H_0$) using both gravitational-wave (GW) and electromagnetic (EM) counterparts. It demonstrates that with next-generation detectors like the Voyager network, $H_0$ can be constrained to better than 2% precision within 5 years, resolving the Hubble tension, while Cosmic Explorer could achieve sub-percent-level precision using NSBH gray sirens alone.

ABSTRACT

The measurement of the Hubble-Lemaître constant $(H_0)$ from the cosmic microwave background and the Type IA supernovae are at odds with each other. One way to resolve this tension is to use an independent way to measure $H_0$. This can be accomplished by using gravitational-wave (GW) observations. Previous works have shown that with the onset of the next-generation of GW detector networks, it will be possible to constrain $H_0$ better than $2\%$ (which is enough to resolve the tension) with binary black hole systems, also called dark sirens. Bright sirens like binary neutron star systems can also help resolve the tension if both the GW and the following electromagnetic counterpart are detected. In this work, we assess the potential of using neutron star-black hole (NSBH) mergers to measure the Hubble-Lemaître constant, both as dark sirens as well as bright sirens, thus, assigning them the term gray sirens. We find that the Voyager network might be able to resolve the tension using NSBH mergers in an observation span of 5 years, whereas next-generation networks which include the Cosmic Explorer detectors and the Einstein Telescope will be able to measure the $H_0$ to sub-percent level.

Motivation & Objective

• To evaluate the potential of neutron star-black hole (NSBH) mergers as independent $H_0$ distance indicators to resolve the Hubble-Lemaître tension.
• To assess both dark siren (statistical) and bright siren (EM counterpart) methods for $H_0$ measurement using NSBH systems.
• To determine the required observation times and detector sensitivities needed to achieve $H_0$ constraints below 2% precision.
• To quantify the impact of neutron star equation of state (EOS), population models, and merger rates on $H_0$ measurement performance.

Proposed method

• The study employs the Fisher Information Matrix (FIM) to estimate $H_0$ measurement precision from NSBH gravitational-wave signals across multiple detector networks.
• It models two population scenarios (Pop-1 and Pop-2) with varying local merger rates and neutron star equations of state (ALF2, APR4, DD2) to assess robustness.
• For bright siren analysis, kilonova (KN) light curves are generated using numerical relativity fits to predict detectability by the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope.
• The analysis combines dark siren (sky localization + galaxy catalog matching) and bright siren (EM counterpart detection) approaches to estimate $H_0$ constraints.
• It evaluates multiple detector networks: HLVKI+, VK+HLIv (Voyager), and ECS (Cosmic Explorer) with Einstein Telescope, across 5- and 10-year observation spans.
• The study computes expected event rates and $H_0$ precision bounds for all combinations of population model, EOS, and detector network.

Experimental results

Research questions

• RQ1 Can NSBH mergers serve as effective standard sirens for $H_0$ measurement using both gravitational-wave and electromagnetic data?
• RQ2 What is the minimum observation time required for next-generation GW networks to resolve the Hubble-Lemaître tension using NSBH gray sirens?
• RQ3 How does the neutron star equation of state affect the detectability of kilonova counterparts and subsequent $H_0$ precision?
• RQ4 To what extent do dark siren and bright siren methods complement each other in $H_0$ estimation using NSBH systems?
• RQ5 Can future detector networks like Cosmic Explorer achieve sub-percent-level $H_0$ precision using only NSBH mergers?

Key findings

• The Voyager network (VK+HLIv) can resolve the Hubble-Lemaître tension within 5 years of observation using NSBH gray sirens, achieving $H_0$ precision below 2%.
• The Cosmic Explorer (ECS) network can measure $H_0$ to better than 1% precision within 2 years using NSBH mergers, with 10–30 high-quality gray siren events detected annually.
• For the APR4 equation of state, HLVKI+ cannot resolve the tension in 5 years, but networks with the Einstein Telescope or Cosmic Explorer detectors can.
• NSBH systems are effective as both golden dark sirens and bright sirens, justifying the term 'gray sirens' due to their dual capability.
• Next-generation networks like ECS are robust to neutron star equation of state uncertainties, as $H_0$ precision is dominated by golden dark siren measurements.
• The study estimates that ECS will detect 10–30 NSBH gray siren events per year, including 1–3 exceptional bright siren events per year that individually achieve $H_0$ precision below 2%.