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REVIEW 3 major objections 4 minor 2 cited by

This paper forecasts that cross-correlating future galaxy surveys with gravitational-wave 'dark sirens' can measure the Hubble constant to 0.7% with third-generation detectors, enough to weigh in on the Hubble tension.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review

2026-08-04 10:42 UTC pith:TUTP5LNO

load-bearing objection Solid conditional forecast of galaxy × dark-siren cross-correlation; the MCMC results give sub-percent H0 for 3G detectors, but the abstract's completeness claim overreaches and the headline sensitivity depends on idealized detector localization. the 3 major comments →

arxiv 2510.08699 v2 pith:TUTP5LNO submitted 2025-10-09 astro-ph.CO gr-qc

Inferring cosmological parameters from galaxy and dark sirens cross-correlation

Giona Sala , Alessandro Cuoco , Julien Lesgourgues , Konstantinos-Rafail Revis , Lorenzo Valbusa Dall'Armi , Santiago Casas This is my paper
classification astro-ph.CO gr-qc
keywords dark sirensgravitational wave cosmologycross-correlationangular power spectrumHubble constantlarge-scale structurestandard sirensforecast
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that the angular cross-correlation between a galaxy catalogue and a catalogue of gravitational-wave events without measured redshifts, known as dark sirens, forms a cosmological probe that does not require the galaxy catalogue to list the host galaxy of every event. Using a full likelihood with Monte Carlo Markov Chain forecasts for ten years of data from existing and planned detectors, crossed with a Euclid-like photometric galaxy survey, the authors find that third-generation detectors can measure the Hubble constant to 0.7% when all auto- and cross-power spectra are combined, and to about 1% from the cross-correlation alone. The core claim is that this precision is enough to discriminate between current conflicting Hubble constant measurements, and that the cross-correlation and galaxy auto-correlation have complementary degeneracy directions that sharpen constraints on other cosmological parameters.

Core claim

Treating galaxies and dark sirens as two linearly biased tracers of the same matter density field, the paper computes the galaxy auto-spectrum, the dark-siren auto-spectrum, and their cross-spectrum, using tomographic bins in galaxy redshift and in gravitational-wave luminosity distance. It shows through a full MCMC likelihood forecast that, with a ten-year dataset from the Einstein Telescope and Cosmic Explorer network and a Euclid-like photometric galaxy catalogue, the galaxy–GW cross-correlation alone constrains H0 to about 1%, while the full covariance including galaxy auto-correlation and GW auto-correlation reaches 0.7%. The same formalism yields only about 30% precision with the curre

What carries the argument

The central object is the set of angular power spectra between galaxy overdensity maps and gravitational-wave event maps: the galaxy auto-spectrum GG, the GW auto-spectrum WW, and the cross-spectrum WG. The cross-spectrum is built in the Limber approximation from window functions placed in redshift bins for galaxies and luminosity-distance bins for GWs, with distance errors and a Gaussian beam of width sigma_Wi describing angular localization folded in. The load-bearing step is that the GW window function converts luminosity distance to redshift using an assumed cosmology, so the likelihood favors the Hubble constant for which the two maps overlap; finite angular localization enters as a bea

Load-bearing premise

The forecasts treat the assumed sky-position and distance errors of gravitational-wave events as the true performance of the planned detectors; if third-generation detectors localize events worse than assumed, both the 1% cross-correlation and 0.7% full-matrix H0 errors would grow.

What would settle it

Rerun the full MCMC likelihood on the same simulated galaxy and GW catalogues after replacing the angular-localization model with localization errors from an independent, end-to-end simulation of the Einstein Telescope and Cosmic Explorer network; the central claim fails if the resulting H0 uncertainty from the full matrix exceeds about 1.5%.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • With a decade of third-generation detector data and a Euclid-like photometric survey, H0 can be measured to 0.7% percent from the full covariance and about 1% from the galaxy–GW cross-correlation alone, a precision that could discriminate between current local and early-universe determinations.
  • The current LIGO-Virgo-KAGRA network gives only about 30% H0 precision, and adding LIGO India improves it to about 7%, so angular localization power, not raw event rate, is the limiting factor for this method.
  • Because the degeneracy directions of the cross-correlation and the galaxy auto-correlation are nearly orthogonal in the h-omega_b and h-omega_cdm planes, the combined analysis yields tighter constraints on matter and baryon densities than either probe provides alone.
  • The dark-siren bias parameters cannot be pinned down by the cross-correlation alone; galaxy auto-correlation information is needed to break the degeneracies and unlock the cosmological content of the cross-spectrum.
  • Black-hole and neutron-star mergers give comparable H0 constraints in the forecast, with black holes slightly better, so including both populations is useful but not the decisive factor for the headline precision.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A testable extension is to rerun the same forecast with a more pessimistic angular-localization model, for example doubling sigma_W(z) at high redshift; if the cross-correlation precision degrades from 1% to several percent, the method's headline power rests more on localization assumptions than on the cross-correlation idea itself.
  • Because the method uses galaxy positions purely as a tracer field rather than requiring the catalogue to contain the true host galaxy, it could be combined with spectroscopic or HI intensity-mapping surveys, which have different noise and redshift properties, to cross-check the photometric result and tighten the GW bias constraints.
  • The same luminosity-distance window function formalism could be applied to other redshift-free source maps, such as fast radio bursts or future directional dark matter detectors, whenever the observable provides a noisy distance proxy.
  • A practical intermediate check before full third-generation data is to run the forecast for 3 and 5 years of data; if the cross-correlation H0 error crosses the 1% threshold substantially before ten years, the conclusion is more robust than the headline assumption of a full decade.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper develops a tomographic angular-power-spectrum formalism for cross-correlating future gravitational-wave (GW) dark-siren catalogs with photometric galaxy catalogs, and uses it to forecast cosmological constraints. The authors model galaxies and GW sources as linearly biased tracers of the matter field, include redshift/DL binning, a Gaussian likelihood for the C_L vector, and MCMC sampling over the flat LCDM parameters plus three bias nuisance parameters. They consider three detector configurations (HLVK, HLVIK, ET2CE) with 10 yr of observation, using GWFast for detection and Fisher-based distance errors and adopting angular resolutions from Ref. [41]. The headline result is that the ET2CE configuration yields a forecast H0 precision of about 1% from the GW-galaxy cross-correlation alone, improving to about 0.7% when the full GG+WW+XC covariance is used. The paper also reports complementarity between the probes and gives a BBH/BNS breakdown.

Significance. If the forecast holds, the method offers a standard-siren H0 measurement that is independent of EM counterparts and of host-galaxy catalog completeness, and could reach the precision needed to address the Hubble tension. The paper's strengths are its full-likelihood MCMC approach, the validation of the C_L-based likelihood against an a_lm-based likelihood in Fig. 10, and the transparent treatment of the angular-resolution degradation in Fig. 5. The forecast is explicitly conditional on the assumed GW detection and localization model, the Euclid-like galaxy selection function, and flat LCDM; within those conditions, the central claim appears defensible. The main weaknesses are internal equation inconsistencies and an overstatement of the completeness insensitivity, both of which are local and fixable.

major comments (3)
  1. [§2, Eqs. (2.3)–(2.5) vs. Eqs. (2.18)–(2.20)] The window-function definitions contain an extra factor H(z). With W_Ai=(dn_Ai/dz)H(z)b_A, substitution into Eq. (2.2) gives spectra H(z)^2 larger (for GG) than the explicit expressions in Eqs. (2.18)–(2.20). The explicit expressions are the standard Limber forms if W_Gi=(dn_Gi/dz)b_G and W_Wi=(dn_Wi/dD_L)(dD_L/dz)b_W. As printed, the two sets of equations are mutually inconsistent and a reader cannot reproduce the calculation. Please remove the H(z) from Eqs. (2.3)–(2.5), or state the intended convention explicitly.
  2. [§3, Eq. (2.10)] The denominator used to normalize dn_Wi/dD_L integrates dN_G/dz(D'_L) p_err(D'_L,D_L), while the numerator integrates dN_W/dD_L(D'_L) p_err(D'_L,D_L). This appears to be a typo, but as written the printed formula is not the normalized distribution shown in Fig. 4. Please correct the denominator so that it integrates the same source distribution as the numerator.
  3. [Abstract and §6] The claim that the method 'does not suffer from systematic errors related to the incompleteness of the galaxy catalogue' is stronger than what is demonstrated. The forecast assumes a Euclid-like selection function and a photometric redshift error model; an incomplete catalog with an incorrectly modeled selection function would still bias the window functions and the cross-correlation. I suggest rephrasing to 'does not require a complete host-galaxy catalogue' and adding a sentence in the conclusions about residual selection-function systematics.
minor comments (4)
  1. [§5.3 and Table 5] The 0.7% H0 precision is conditioned on the angular localization model from Ref. [41]. Since Fig. 5 shows that the cross-correlation SNR degrades strongly with finite angular resolution, please add an explicit caveat in Section 5.3 or the conclusions, and consider a robustness test with, e.g., a factor-of-two worse σ_Wi(z).
  2. [§4, Eq. (4.4)] A single f_fov is used for all covariance blocks, including the WW block. Because the GW survey is full-sky, the WW auto-spectrum block should formally use f_fov=1. Since the WW constraints are reported as negligible, I expect this has little effect, but please clarify or test the impact.
  3. [§3.1, Table 1] The BNS merger rate at z=0 is the best-fit value from Ref. [5] and has an order-of-magnitude uncertainty. The paper notes this in passing; it would be helpful to state in the conclusions that the headline constraints are dominated by BBH and robust to this uncertainty.
  4. [§5.3.1 and Fig. 8] There is a small typo: 'BBN+BBH' in the text/figures should be 'BBH+BNS' or 'combined'. Please check the wording.

Circularity Check

0 steps flagged

No significant circularity: the 0.7% H0 result is an output of a conditional sensitivity forecast, not a consequence of defining the prediction from its own inputs.

full rationale

The derivation chain is: (i) §2 defines the auto/cross C_ell from linear bias and Limber integrals, with window functions that include the photometric redshift and GW distance uncertainties; (ii) §3 generates the GW source distributions, distance errors, and angular localizations from GWFast plus the external [41] angular-resolution results; (iii) §4 sets the mock data vector equal to the theory vector at the fiducial cosmology and builds the Gaussian covariance from the same theory plus noise; (iv) §5 runs MCMC over cosmological and bias parameters. Every listed element is an input assumption of a sensitivity forecast. The H0 posterior is an output of the likelihood curvature: h is varied over a wide prior ([0.1,1.5], Table 3) and is recovered with non-trivial width (Tables 5-6), so the 0.7% error is not forced by construction. The only self-citation entering the input chain, [41] for sigma_Wi(z), is an external published calculation, and the paper explicitly cross-checks it against GWFast-derived values: "We verified that the GWFast-derived sigma[s](z) are in reasonable agreement with the ones from [41] that we actually use." That makes it independent support rather than load-bearing self-citation. Limitations are disclosed, not hidden: the HL VK angular localization is flagged as "slightly optimistic" because it reuses the HL VIK value, and Figure 5 explicitly shows the critical impact of the beam on SNR. No equation reduces to its own input, no fitted parameter is renamed as a prediction, and no uniqueness theorem from the authors is invoked. The broad phrase "does not suffer from systematic errors related to the incompleteness of the galaxy catalogue" is a methodological argument rather than a derived numerical claim; any concern there is about overclaiming, not circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 0 invented entities

The forecast rests on a chain of modeling choices: the assumed cosmology, bias model, survey specifications, and GW measurement errors. The headline precision is conditional on all of these; the paper only marginalizes over the three bias parameters and five cosmological parameters, not over the model itself.

free parameters (4)
  • GW dN/dL analytic fit coefficients (a,b,c,d) = Table 1, e.g. ET2CE BBH a=9.40e-7, b=2.15, c=3.76e-4, d=0.870
    Eq. (3.8) fits the simulated GW redshift/distance distributions; the fitted event counts and redshift shapes directly set the covariance and SNR.
  • aG1 (galaxy bias normalization) = 1.0 (fiducial)
    Nuisance parameter varied in MCMC; hand-picked fiducial with flat prior [0.5,2.0].
  • aW1 (GW bias normalization) = 2.0 (fiducial)
    Nuisance parameter varied in MCMC; hand-picked fiducial with flat prior [0,4].
  • aW2 (GW bias slope) = 0.0 (fiducial)
    Nuisance parameter varied in MCMC; hand-picked fiducial with flat prior [-2,7].
axioms (7)
  • domain assumption Flat ΛCDM with fiducial parameters (Table 3) is the true model; mock data and theory use the same cosmology.
    The likelihood and simulated data assume this cosmology; Appendix A gives a curved extension but it is not used.
  • domain assumption Galaxies and GW sources are linear biased tracers of dark matter with bias parameterizations b_G(z)=aG1/sqrt(1+z) and b_W(z)=aW1(1+z)^aW2.
    Enter at Eqs. (2.12)-(2.13); the forecast marginalizes over the bias parameters but not over the functional form.
  • domain assumption Limber approximation Eq. (2.2) is valid for ℓ in [2,1000].
    All auto/cross power spectra use the Limber approximation; the paper does not quantify its error at low ℓ.
  • domain assumption GW angular resolution and distance errors from [41]/GWFast represent future detector performance.
    Uses Fig. 3 values in Eq. (2.15); Fig. 5 shows results are critically sensitive to angular resolution.
  • domain assumption Euclid-like photometric survey: 30 arcmin^-2 galaxy density, 5% photo-z errors, 10% outliers.
    Eqs. (2.7)-(2.9); the galaxy window functions and shot noise depend on these survey specifications.
  • domain assumption BBH/BNS merger rates follow the UniverseMachine SFR with a 1/t_d delay and are normalized to LVK z=0 rates.
    Eq. (3.4); the forecasted event counts, especially BNS counts, depend on this population model.
  • domain assumption C_l-based Gaussian likelihood (Eq. 4.1) is a sufficient approximation to the full a_lm likelihood.
    Validated for one case in Fig. 10; used for all forecasts.

pith-pipeline@v1.3.0-alltime-deepseek · 26846 in / 18211 out tokens · 152221 ms · 2026-08-04T10:42:40.269967+00:00 · methodology

0 comments
read the original abstract

The number of observed gravitational wave (GW) events is growing fast thanks to rapidly improving detector sensitivities. GWs from compact binary coalescences like Black Holes or Neutron Stars behave like standard sirens and can be used as cosmological probes. To this aim, generally, the observation of an electromagnetic counterpart and the measurement of the redshift are needed. However, even when those are not available, it is still possible to exploit these "dark sirens" via statistical methods. In this work, we explore a method that exploits the information contained in the cross-correlation of samples of GW events with matter over-density tracers like galaxy catalogues. Contrary to other currently employed dark-sirens methods, this approach does not suffer from systematic errors related to the incompleteness of the galaxy catalogue. To further enhance the technique, we implement tomography in redshift space for the galaxy catalogue and luminosity distance space for the GWs. We simulate future data collected by the array of currently existing detectors, namely LIGO, Virgo, and Kagra, as well as planned third-generation ones such as the Einstein Telescope and Cosmic Explorers. We cross-correlate these data with those from upcoming photometric galaxy surveys such as Euclid. We perform a sensitivity forecast employing a full-likelihood approach and explore the parameter space with Monte Carlo Markov Chains. We find that with this method, third-generation detectors will be able to determine the Hubble constant $H_0$ with an error of only 0.7%, which is enough to provide decisive information to shed light on the Hubble tension. Furthermore, for the other cosmological parameters, we find that the GWs and galaxy surveys information are highly complementary, and the use of both significantly improves the ability to constrain the underlying cosmology.

discussion (0)

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dark siren cross-correlations and the sensitivity of $H_0$ to methodological choices

    astro-ph.CO 2026-05 conditional novelty 5.0

    Methodological choices in dark-siren angular cross-correlations can bias H0, but forward-modelling selection, flexible bias, mock covariances and sensible binning keep the recovery unbiased for large precise samples.

  2. Dark siren cross-correlations and the sensitivity of $H_0$ to methodological choices

    astro-ph.CO 2026-05 unverdicted novelty 4.0

    Methodological choices in dark siren cross-correlations can mitigate biases in H0 inference when selection effects are built into the model and samples of precise events are sufficiently large.

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.