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Combining 142 GW standard sirens with TDCOSMO2025 lensing data constrains model-independent H0 to 83.78 km s^{-1} Mpc^{-1} at 13.58% precision.

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T0 review · grok-4.3

2026-06-28 08:35 UTC pith:QBZVXTPJ

load-bearing objection The H0 result shifts from 84 to 75 km/s/Mpc and precision from 14% to 5.6% depending on the lensing mass-sheet treatment. the 1 major comments →

arxiv 2606.03634 v1 pith:QBZVXTPJ submitted 2026-06-02 astro-ph.CO gr-qchep-ph

Model-independent H0 from GWTC-4 standard sirens and TDCOSMO 2025 strong lensing time delays

En-Yu Xiong , Ji-Yu Song , Jing-Fei Zhang , Xin Zhang This is my paper
classification astro-ph.CO gr-qchep-ph
keywords Hubble constantstandard sirensstrong lensingtime delaysmodel-independent cosmologyHubble tensiondistance sum rulegravitational waves
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.

This paper establishes a model-independent value for the Hubble constant by merging gravitational-wave standard siren measurements from GWTC-4 with TDCOSMO2025 strong lensing time delays via the distance sum rule. A reader would care because both sides of the Hubble tension depend on model assumptions, so an assumption-free route could help resolve the discrepancy. The central result under the FullPop-4.0 model and TDCOSMO2025 lensing setup is H0 = 83.78 with asymmetric errors giving 13.58 percent precision. Precision is shown to be limited mainly by the lensing side's handling of mass-sheet transformations, as switching methods changes the outcome substantially. Current values align with both Planck and SH0ES, with expectations that more data will refine the test.

Core claim

In this work, 142 gravitational-wave standard siren events from GWTC-4 are combined with the latest TDCOSMO2025 time-delay strong lensing data to constrain H0 using a cosmological-model-independent framework based on the distance sum rule. With the FullPop-4.0 population model and TDCOSMO2025-only lensing configuration, H0 is measured as 83.78^{+12.53}_{-10.23} km s^{-1} Mpc^{-1} at 13.58% relative precision. The precision depends primarily on the mass-sheet transformation treatment, and switching to the H0LiCOW method yields a tighter constraint of 75.42^{+3.74}_{-4.66} km s^{-1} Mpc^{-1} at 5.57% precision. All results remain consistent with both Planck and SH0ES values at the current leve

What carries the argument

The distance sum rule, which enables the combination of luminosity distances from gravitational waves and angular diameter distances from strong lensing time delays to infer H0 without assuming a specific cosmological model.

Load-bearing premise

The specific treatment of the mass-sheet transformation in the strong-lensing analysis does not introduce significant systematic errors in the inferred distances.

What would settle it

Obtaining additional gravitational wave events or lensing systems that shift the combined H0 value outside the reported error bars while using the same analysis framework would falsify the current constraint.

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

If this is right

  • Results are consistent with both Planck and SH0ES at current precision.
  • Changing the lensing analysis method from TDCOSMO2025 hierarchical to H0LiCOW changes the central value and tightens the uncertainty significantly.
  • More high-redshift dark siren events and additional time-delay lens systems will improve the precision of this model-independent H0 measurement.

Where Pith is reading between the lines

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

  • This combination method could provide an independent check on the Hubble tension if future data increases precision enough to separate the early and late universe values.
  • The sensitivity to lensing analysis choices suggests that standardizing mass-sheet transformation treatments across studies is key for reliable model-independent results.
  • Extending this to higher redshifts might reveal if any tension is due to model assumptions or new physics.

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

1 major / 0 minor

Summary. The manuscript combines 142 gravitational-wave standard siren events from GWTC-4 with TDCOSMO2025 strong-lensing time-delay data to constrain H0 via the distance sum rule in a cosmological-model-independent framework. Under the FullPop-4.0 population model and the TDCOSMO2025-only lensing configuration, the central result is H0 = 83.78^{+12.53}_{-10.23} km s^{-1} Mpc^{-1} (13.58% relative precision). The abstract also reports that replacing the TDCOSMO2025 hierarchical mass-sheet treatment with the H0LiCOW method shifts the result to H0 = 75.42^{+3.74}_{-4.66} km s^{-1} Mpc^{-1} (5.57% precision). All quoted values remain consistent with both Planck and SH0ES within current uncertainties.

Significance. If the central claim is robust to the lensing analysis choices, the work provides a useful model-independent cross-check on H0 that avoids both early-Universe assumptions and late-Universe distance-ladder calibrations. The use of the distance sum rule and the large GW sample are strengths. However, the reported precision is shown to be governed by the mass-sheet transformation treatment, which limits the immediate impact on the Hubble tension until that systematic is better controlled or marginalized.

major comments (1)
  1. [Abstract] Abstract: The primary quoted result (H0 = 83.78^{+12.53}_{-10.23}, 13.58% precision) is conditional on the TDCOSMO2025 hierarchical mass-sheet framework. The manuscript itself demonstrates that adopting the H0LiCOW treatment instead produces a substantially different central value and tighter uncertainty (75.42^{+3.74}_{-4.66}, 5.57%). Because the distance-sum-rule combination inherits the lensing distance posteriors directly, this choice is load-bearing for both the reported precision and the interpretation of consistency with Planck/SH0ES; the paper should either adopt a single justified framework with explicit justification or propagate the difference as a systematic uncertainty on the main result.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting an important point regarding the presentation of our results. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The primary quoted result (H0 = 83.78^{+12.53}_{-10.23}, 13.58% precision) is conditional on the TDCOSMO2025 hierarchical mass-sheet framework. The manuscript itself demonstrates that adopting the H0LiCOW treatment instead produces a substantially different central value and tighter uncertainty (75.42^{+3.74}_{-4.66}, 5.57%). Because the distance-sum-rule combination inherits the lensing distance posteriors directly, this choice is load-bearing for both the reported precision and the interpretation of consistency with Planck/SH0ES; the paper should either adopt a single justified framework with explicit justification or propagate the difference as a systematic uncertainty on the main result.

    Authors: We agree that the mass-sheet transformation treatment is load-bearing for the reported precision and central value, as the manuscript already demonstrates by presenting both results. We selected the TDCOSMO2025 hierarchical framework as the primary quoted result because it constitutes the latest analysis from the TDCOSMO collaboration and employs a hierarchical Bayesian treatment that more conservatively marginalizes over the mass-sheet degeneracy. The H0LiCOW result is shown explicitly to illustrate the impact of this choice. To address the referee's concern, we will revise the abstract to provide a clearer justification for adopting TDCOSMO2025 as the baseline and to frame the H0LiCOW result as the key systematic variation. We do not believe full propagation as an additional systematic uncertainty is required at this stage, given that both frameworks are already reported side-by-side with their respective posteriors. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation combines independent datasets via geometric sum rule

full rationale

The paper derives H0 by combining GW standard-siren luminosity distances (from GWTC-4 events under the external FullPop-4.0 population model) with TDCOSMO2025 time-delay distances via the distance sum rule, a purely geometric relation independent of any cosmological model or the target H0. The text explicitly contrasts two lensing treatments (TDCOSMO2025 hierarchical vs. H0LiCOW) and reports how each shifts the posterior, demonstrating transparency rather than concealment. No equation or section shows a fitted parameter being relabeled as a prediction, a self-citation supplying a uniqueness theorem, or an ansatz smuggled in; the central claim therefore remains non-circular and externally falsifiable against Planck/SH0ES.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only review prevents exhaustive enumeration; the ledger records only elements explicitly named in the abstract.

free parameters (1)
  • FullPop-4.0 population model parameters
    Referenced as the siren population model; parameters are not stated but are required to convert observed events into distance posteriors.
axioms (2)
  • domain assumption Distance sum rule relates luminosity distances and time-delay distances without requiring a specific expansion history
    Invoked to achieve model independence.
  • domain assumption TDCOSMO2025 time-delay measurements and GWTC-4 events are statistically independent
    Required for joint likelihood.

pith-pipeline@v0.9.1-grok · 5856 in / 1565 out tokens · 27129 ms · 2026-06-28T08:35:42.658928+00:00 · methodology

0 comments
read the original abstract

The significant discrepancy between early- and late-Universe measurements of the Hubble constant, known as the Hubble tension, remains one of the most pressing open questions in cosmology. Since both sides of the tension rely on model-dependent assumptions or multi-rung calibration chains, a cosmological-model-independent measurement of $H_0$ is essential to arbitrate this discrepancy. In this work, we combine 142 gravitational-wave standard siren events from the Fourth Gravitational-Wave Transient Catalog with the latest TDCOSMO2025 time-delay strong lensing data to constrain $H_0$ in a cosmological-model-independent framework based on the distance sum rule. Under the FullPop-4.0 population model with the TDCOSMO2025-only lensing configuration, we obtain $H_0 = 83.78^{+12.53}_{-10.23}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, with a relative precision of $13.58\%$. We find that the $H_0$ precision is governed primarily by the mass-sheet transformation treatment on the strong-lensing side: replacing the conservative TDCOSMO2025 hierarchical framework with the H0LiCOW method tightens the constraint to $H_0 = 75.42^{+3.74}_{-4.66}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, with a relative precision of $5.57\%$. At the current precision, all results are consistent with both the Planck and SH0ES values, and future improvements from more high-redshift dark siren events and more time-delay lens systems are expected to strengthen this model-independent approach.

Figures

Figures reproduced from arXiv: 2606.03634 by En-Yu Xiong, Jing-Fei Zhang, Ji-Yu Song, Xin Zhang.

Figure 1
Figure 1. Figure 1: Distribution of the GW standard siren samples and [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Joint posterior distributions of H0, the popula￾tion mean of the internal MST parameter λint,0, and the slope αλ describing the dependence of λint on Reff /θE, ob￾tained from the GWTC-4 + TDCOSMO2025-only analysis with third-order polynomial distance reconstruction. The in￾ner and outer contours enclose the 68.3% and 90% credible regions, respectively. age points, reflecting both the larger event sample an… view at source ↗
Figure 3
Figure 3. Figure 3: One-dimensional posterior distributions of [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

discussion (0)

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Forward citations

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Reference graph

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