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Cosmology beyond standard sirens: cross-correlation of gravitational waves and neutral hydrogen intensity mapping

This paper demonstrates that cross-correlating gravitational wave events from future detectors like the Einstein Telescope with neutral hydrogen intensity mapping from the SKAO provides a robust, systematic-mitigated cosmological probe capable of constraining the Hubble constant to sub-percent precision and measuring matter density and clustering amplitude with high accuracy.

Original authors: Matteo Schulz, Ulyana Dupletsa, Andrea Cozzumbo, Giona Sala, Tommaso Ronconi, Marta Spinelli, Riccardo Murgia, Simone Mastrogiovanni, Jan Harms, Erik de la Haye, Felicitas Keil

Published 2026-07-30

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Matteo Schulz, Ulyana Dupletsa, Andrea Cozzumbo, Giona Sala, Tommaso Ronconi, Marta Spinelli, Riccardo Murgia, Simone Mastrogiovanni, Jan Harms, Erik de la Haye, Felicitas Keil

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding balloon covered in a sticky, invisible fog. For decades, scientists have been trying to measure exactly how fast this balloon is inflating and how the fog is clumping together. They use two main tools: looking at the faint afterglow of the Big Bang (like a baby picture of the universe) and watching distant exploding stars (like cosmic lighthouses). But here's the problem: when they measure the speed of the expansion using these different methods, they get slightly different answers. It's like two friends measuring the same room with different rulers and getting different numbers. This disagreement, known as the "Hubble tension," is one of the biggest mysteries in modern physics. To solve it, scientists need a brand-new, independent way to measure the universe that doesn't rely on the old tools. They need a way to see the universe that is completely different from everything else.

Enter the "standard siren." Just as a lighthouse gives off light, crashing black holes give off gravitational waves—ripples in the fabric of space-time. These ripples tell us exactly how far away the crash happened, but they are silent about when it happened. It's like hearing a siren in the distance; you know how loud it is (distance), but you don't know if it's a fire truck or a police car (redshift/age) without seeing it. Usually, scientists try to find the "visual" partner of the crash, but black holes are often "dark," meaning they don't flash any light. This paper proposes a clever workaround: instead of looking for a light, let's listen to the "fog" around the crash. By matching the location of the gravitational wave crash with a map of neutral hydrogen (the foggy gas that fills the universe), we can figure out exactly how far away and how old the crash is, all without needing a telescope to see the light.

The Cosmic Detective Game

This paper is a forecast—a detailed simulation of a future detective game played by two massive, next-generation observatories: the Einstein Telescope (ET), which will listen for gravitational waves, and the SKA Observatory (SKAO), which will map the neutral hydrogen fog. The authors, a team of cosmologists, asked a simple question: If we cross-reference the "sound" of crashing black holes with the "map" of the hydrogen fog, can we solve the mystery of the universe's expansion?

They simulated what would happen if these observatories were built and started working together. The idea is that both the crashing black holes and the hydrogen gas are like tracers floating in the same dark matter "soup." Even though we can't see the soup, we know the black holes and the gas tend to clump together in the same places. By looking at how the gravitational wave events and the hydrogen gas overlap in the sky, the team can figure out the true distance to the black holes.

The Results: A New Kind of Precision

The simulation showed that this "cross-correlation" method is incredibly powerful. Here is what they found:

Solving the Distance Puzzle: When they used just the gravitational waves alone, the results were a bit fuzzy, like trying to guess a location with a blurry map. But when they added the hydrogen map, the picture snapped into focus. The method successfully broke the confusion between distance and time, allowing them to measure the Hubble constant (the speed of the universe's expansion) with a precision of about 0.5%. That is incredibly sharp—sharper than many current methods.
The Power of Three: The team tested different setups for the gravitational wave detectors. They found that a single detector or even two nearby ones weren't quite enough to get the best results. However, when they combined two Einstein Telescopes with a third giant detector called Cosmic Explorer (a setup they call ET2L+CE), the results were spectacular. This trio of detectors, working together, provided the "golden" baseline for their measurements.
Seeing the Invisible Clumps: Unlike older methods that only told them how fast the universe is expanding, this new method also told them how the "clumps" of matter in the universe are growing. They were able to measure the "clustering amplitude" (how tightly matter is packed together) with a precision of about 1.6%. This is a huge deal because it lets scientists test if the universe is behaving exactly as our current theories predict, or if there is some new, weird physics at play.
Robustness Against Errors: One of the coolest parts of this method is that it is naturally resistant to mistakes. Because the gravitational waves and the hydrogen maps are measured by completely different instruments (one listens to space ripples, the other listens to radio waves), any errors or "noise" in one system don't mess up the other. It's like two people trying to solve a puzzle; if one drops a piece, the other still has theirs, and they can still see the picture.

What This Means for Us

The authors are careful to note that these results are based on simulations of future technology, not measurements from today. They haven't built the Einstein Telescope or the full SKA yet. However, their math shows that if we build these machines, we will have a powerful new tool to understand the universe.

They also point out that while the hydrogen data does most of the heavy lifting in this specific simulation, the gravitational waves provide a crucial "independence." This means the final answer isn't just a repeat of what we already know from other methods; it's a fresh, independent check. If the universe is indeed expanding at the rate they predict, this method will confirm it. If the universe is doing something weird, this method will be the first to catch it.

In short, this paper suggests that by listening to the "music" of crashing black holes and looking at the "fog" of hydrogen gas at the same time, we might finally get a clear, high-definition view of how our universe is growing and changing. It's a promising step toward solving the biggest riddle in cosmology, turning a blurry guess into a precise measurement.

Technical Summary: Cosmology beyond standard sirens: cross-correlation of gravitational waves and neutral hydrogen intensity mapping

Problem Statement
Current cosmological probes, such as the Cosmic Microwave Background (CMB) and Type Ia Supernovae, have reached sub-percent precision, yet discrepancies persist between early- and late-universe measurements of parameters like the Hubble constant ( $H_0$ ), known as the "Hubble tension." While Gravitational Waves (GWs) from binary black hole (BBH) mergers offer a "standard siren" method to measure luminosity distances independently of the cosmic distance ladder, they suffer from a fundamental degeneracy between source redshift and measured mass. Breaking this degeneracy typically requires electromagnetic counterparts ("bright sirens") or statistical association with galaxy catalogs ("dark sirens"). However, these methods often rely on specific host galaxy identification or assume Gaussian posteriors, which can limit precision and introduce systematic biases. Furthermore, conventional standard siren techniques are primarily sensitive to background expansion history ( $H_0$ , $\Omega_m$ ) but lack sensitivity to the growth of cosmic structures ( $\sigma_8$ ).

Methodology
The authors propose a cross-correlation method between GW events and Neutral Hydrogen (HI) Intensity Mapping (IM) surveys to serve as an independent cosmological probe. The core physical assumption is that both BBH mergers and HI emission are biased tracers of the same underlying dark matter distribution. Consequently, their spatial clustering should exhibit a non-zero angular cross-correlation signal that peaks when the assumed cosmological model correctly maps GW luminosity distances to the redshifts of the HI tracer.

Key methodological components include:

Tracers and Observatories: The study focuses on the synergy between the Einstein Telescope (ET) for GWs and the SKA Observatory (SKAO) for HI IM. Three GW network configurations are tested: ET alone ( $\Delta$ configuration), ET in a dual-site 2L configuration, and ET-2L combined with a 40 km Cosmic Explorer (CE).
Tomographic Angular Power Spectra: The authors compute the angular auto- and cross-correlation spectra ( $C_\ell$ ) using a fully relativistic treatment that goes beyond the Limber approximation. They utilize a custom fork of Multi_CLASS to calculate exact integrals.
Redshift Binning: A tomographic approach is employed. HI is binned in fixed narrow redshift intervals ( $\Delta z = 0.1$ ), while GW bins are defined to contain an approximately equal number of sources across the redshift range $0.5 \le z \le 3.5$ to ensure uniform statistical weight.
Bias and Noise Modeling: The analysis incorporates three bias terms for both tracers: selection bias, magnification bias, and evolution bias. Noise models account for shot noise (dominant for GWs), instrumental noise, and foreground residuals (dominant for HI). Crucially, the cross-correlation signal is shown to naturally cancel out tracer-specific systematics (e.g., foregrounds in radio and localization errors in GWs) because these errors are uncorrelated between the two datasets.
Parameter Estimation: The authors employ a full Bayesian Markov Chain Monte Carlo (MCMC) framework using MontePython. They analyze the likelihood of the angular power spectra to constrain cosmological parameters within the $\Lambda$ CDM model, specifically varying $H_0$ , the physical CDM density $\omega_{cdm}$ , and the primordial power spectrum amplitude $\ln(10^{10}A_s)$ . Derived parameters include the total matter density $\Omega_m$ and the clustering amplitude $\sigma_8$ .

Key Contributions

Robustness to Systematics: The paper demonstrates that the cross-correlation method inherently mitigates observational and theoretical systematics. Unlike methods relying on the full covariance of a single tracer, the cross-spectrum of independent datasets (GW and HI) causes uncorrelated errors (such as foreground residuals in HI and localization errors in GWs) to vanish.
Simultaneous Probing of Expansion and Growth: Unlike standard siren techniques which are largely sensitive only to background expansion, this method simultaneously probes the growth of matter perturbations. This allows for the simultaneous constraint of geometric parameters ( $H_0, \Omega_m$ ) and the amplitude of matter fluctuations ( $\sigma_8$ ).
Beyond Standard Sirens: The work moves beyond previous Fisher matrix forecasts by utilizing full MCMC analyses and realistic mock catalogs generated with GWFish+Priors, accounting for non-Gaussian posteriors and detector-specific selection effects.
Network Comparison: The study systematically evaluates the impact of different GW detector networks, highlighting that a single-site or dual-site ET configuration lacks sufficient baseline for precise triangulation, whereas the addition of Cosmic Explorer (ET2L+CE) is required to achieve stringent cosmological constraints using only the cross-correlation signal.

Results
The authors present forecasts for the ET2L+CE network combined with SKAO:

Hubble Constant ( $H_0$ ): The "FullMatrix" analysis (combining GW auto-correlation, HI auto-correlation, and GW-HI cross-correlation) achieves a precision of approximately 0.5% on $H_0$ . Remarkably, even using only the GW $\times$ HI cross-correlation term (excluding auto-correlations), the method yields a precision of ~2.9%, which is competitive with current standard siren forecasts and significantly tighter than current dark siren constraints.
Matter Density ( $\Omega_m$ ): The FullMatrix analysis constrains $\Omega_m$ to ~1.2% precision. The isolated cross-correlation yields ~9% precision.
Clustering Amplitude ( $\sigma_8$ ): By freeing the primordial amplitude $A_s$ , the FullMatrix analysis achieves a ~1.6% precision on $\sigma_8$ . The isolated cross-correlation yields ~5.3% precision.
Degeneracy Breaking: The inclusion of HI auto-correlation and cross-correlation breaks the negative $H_0$ - $\Omega_m$ degeneracy typical of GW-only analyses, resulting in a slight positive correlation in the FullMatrix case. The analysis confirms that the pipeline recovers injected fiducial values without bias.

Significance
The paper claims that this cross-correlation technique offers a powerful, independent probe of the Universe's expansion history and structure growth, capable of reaching sub-percent precision on $H_0$ comparable to the Planck CMB and SH0ES distance ladder results. A primary significance is the method's intrinsic robustness; by relying on the statistical combination of independent datasets, it provides cosmological inferences that are highly resilient against unmodeled systematics. Furthermore, the ability to constrain $\sigma_8$ alongside $H_0$ and $\Omega_m$ allows for rigorous tests of the $\Lambda$ CDM model and potential extensions (such as dynamical dark energy) by checking the consistency between background expansion and structure growth. The authors emphasize that while the constraining power is heavily driven by the high-redshift precision of the HI data, the GW cross-correlation is essential for providing a systematic-free validation of these constraints. The developed framework is modular and publicly available, intended to facilitate future multi-tracer analyses with other cosmological probes.

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