One Night to One Percent: How Dark Sirens Measure the Hubble Constant ✛
Context
The Hubble constant is a fundamental parameter that sets the current expansion rate of the universe. Measurements from the cosmic microwave background (Planck satellite) give H0≈67.4 km/s/Mpc, while local methods based on Cepheids and supernovae yield about 73.2 km/s/Mpc. This 5σ discrepancy challenges systematic errors or even the standard cosmological model. Gravitational waves from black hole mergers open a third, independent path—the standard siren method. If an electromagnetic flash is seen after a merger, the distance from the gravitational signal is directly compared with the redshift of the host galaxy, yielding H0. Yet most mergers—so-called dark sirens—have no optical counterpart. Then H0 is inferred statistically: all galaxies within the sky localization region are potential host candidates. For this method to work, complete spectroscopic catalogs are needed; the depth of the catalog crucially affects accuracy and potential biases.
Methods
The authors used cosmological numerical simulation Uchuu-ν2GC, which reproduces the evolution of large-scale structure and galaxy properties. Tens of thousands of injected signals from black hole mergers were embedded into this simulated catalog, with mass, spin, and redshift distributions matching the latest LIGO–Virgo–KAGRA observational data. For each event, Bayesian inference was used to estimate signal parameters and sky localization. Then the events with the best localization accuracy were selected—between 3 and 15 per year of observing. Volume-limited galaxy samples were constructed for these events with different apparent magnitude limits (from r≈17.5 to r≈24). The statistical significance of the results was assessed via bootstrapping—1000 random samples with replacement. Also modeled was the time needed for spectroscopic observations of these fields on large telescopes such as DESI, Subaru/PFS, Magellan/IMACS, and others.
Results
The main result: for the ten best-localized events of the HLI# network (LIGO Hanford, Livingston, and LIGO-India at A# sensitivity), the median H0 accuracy was 0.98% with a catalog limit of r≈19. Deeper catalogs yield virtually no improvement in this accuracy, while shallower ones (r<17.5) lead to underestimated error bars and biases, even to the point of losing events due to lack of suitable galaxies. For the HLV+ network (Hanford, Livingston, Virgo at A+ sensitivity), the median accuracy drops to 2.63%, reflecting poorer localization. The systematic shift in the median H0 value was statistically insignificant (−0.03%). The required spectroscopic time ranged from 1 to 5 nights depending on the instrument and the conservativeness of the estimates. For instance, DESI handles one event in about an hour, while HET/VIRUS needs up to several hours per field. Still, the total time does not exceed a few nights, which is feasible within a standard telescope time proposal.
Implications
This work provides a clear recipe for rapidly resolving the Hubble tension with dark sirens. It shows that there's no need to wait decades and build enormous catalogs—it's enough to focus on rare but exquisitely well-localized events and conduct pointed observations. This approach makes the dark siren method competitive today, using existing LIGO infrastructure and large spectrographs. Moreover, it imposes constraints on modified gravity theories.
Future development
Future gravitational-wave detectors such as the Einstein Telescope and Cosmic Explorer will have orders-of-magnitude better sensitivity and localization, enabling accuracy down to 0.1% and the use of thousands of dark sirens for precision cosmology. Combined with deep surveys from LSST, Euclid, and spectroscopic campaigns from DESI, 4MOST, and PFS, this promises to turn the method into a standard tool for probing dark energy and modified gravity.
Impact
Directly impacts observational cosmology and gravitational wave physics, offering a swift way to calibrate the distance ladder and test the standard ΛCDM cosmological model, including the properties of dark energy.
Next steps
The next step is an actual observing campaign during the upcoming LIGO–Virgo–KAGRA run, prioritizing events localized to better than 1 square degree, using dedicated time on DESI, PFS/Subaru, and Magellan.
Key open problems
Directly connected to the Hubble tension—one of the most acute crises in modern cosmology. The result is also critical for understanding the nature of dark energy, black hole populations, and systematic errors in cosmic distance measurements.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This study explores how the depth of a spectroscopic galaxy catalog affects the accuracy of Hubble constant measurements using the dark siren method. Using Uchuu-ν2GC simulations and LIGO–Virgo–KAGRA signal injections, it shows that for the HLI# network, the median accuracy reaches 0.98% at a catalog threshold of r≈19, and deeper surveys do not yield significant improvements.
Where its strength is
The strength of this work lies in its quantitative assessment of the trade-off between catalog depth and H0 accuracy for realistic detector configurations, including an estimate of the required observing time. This provides practical guidance for planning future campaigns.
Where it could go next
- It may be interesting to compare the obtained constraints with alternative methods for resolving the Hubble tension that use gravitational waves and other messengers, as in a work where two independent cosmological probes are combined into a single analysis.based on: Cosmic Detective: Two Independent Clues Against the Main Cosmological Debate arXiv:2606.03634v1
- A related study considers primordial black holes as a source of dark sirens, which could extend the method's applicability to higher redshifts and test the robustness of galaxy catalog calibration.based on: Cosmic Hot Tap: How Primordial Black Holes Rewrite the Speed of the Universe arXiv:2607.18528v1
- Our archive contains a paper investigating how gravitational sirens can constrain not only H0 but also the curvature of the Universe; this direction could be a natural extension when moving to deeper catalogs and larger statistics.based on: Echoes of Black Holes: How Gravitational Sirens Reveal the Curvature of the Universe arXiv:2606.04216v1
Worth trying
- Investigate how including galaxies with photometric redshifts (instead of purely spectroscopic ones) affects the depth–accuracy trade-off.
- Test the method on simulated data for next-generation networks (Cosmic Explorer, Einstein Telescope), where localization areas will be significantly smaller and catalog requirements may change.
- Using the same simulated catalog, assess whether systematic biases can be reduced by Bayesian weighting of candidate galaxies by their stellar masses or star formation rates.
Why this may matter
The conclusion that a catalog down to r≈19 is sufficient is important for allocating resources in large spectroscopic surveys: it shows that for dark siren cosmology, one does not need to wait for extremely deep catalogs but can rely on existing and planned moderate-depth data, thereby accelerating an independent test of the Hubble tension.
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Original abstract
as written by the authors arXiv:2607.17284v1
Gravitational-wave events from compact binary coalescences (CBCs) can be used as standard sirens: they encode the luminosity distance to their sources, which yields a measurement of the Hubble constant ($$H_0$$) if the source's redshift is known. In the absence of an electromagnetic counterpart, $$H_0$$ can still be inferred statistically from the cataloged galaxies within the event's sky localization volume via the dark siren, or galaxy catalog method. In this work we examine how the depth of a volume-limited galaxy catalog affects this inference and identify the most efficient spectroscopic strategy for an unbiased measurement of $$H_0$$ at a median precision of $$0.98\%$$. The strategy is to carry out spectroscopic surveys to a depth of $$r \sim 19$$ for the ten best-localized events observed in one year by the LIGO Hanford, LIGO Livingston, and LIGO-India network at A$$^\#$$ sensitivity. Such a campaign requires a minimum of one night of electromagnetic follow-up observations, or five nights under the most conservative assumptions. For the Hanford, Livingston, and Virgo network at A$$+$$ sensitivity, the same ten-event strategy yields a median precision of $$2.63\%$$.
About 20% of these well-localized events fall in the Zone of Avoidance, where Milky Way interstellar dust blocks the view, requiring an extended campaign. For some events, shallower catalogs (r<19) turned up zero potential host galaxies, forcing a switch to deeper surveys or outright exclusion.
Key numbers
- median H0 accuracy (HLI#): 0.98%
- H0 accuracy (HLV+): 2.63%
- minimum number of observing nights: 1
- conservative number of nights: 5
- catalog magnitude limit: r=19
- number of best events per year: 10