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arxiv: 2605.28658 · v1 · pith:5HE7PWFUnew · submitted 2026-05-27 · 🌌 astro-ph.CO

Measuring the Hubble constant with strongly lensed gravitational waves from space-based detector networks

Yong Yuan , Minghui Du , Wen-Fan Feng , Benyang Zhu , Qing Diao , Peng Xu , Xilong Fan This is my paper

Pith reviewed 2026-06-29 10:35 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords strongly lensed gravitational wavesHubble constantspace-based detectorsTaijiLISAbinary black hole mergersgravitational lensingcosmology
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The pith

Strongly lensed gravitational waves observed by space-based detector networks can constrain the Hubble constant even when source redshifts are unknown, provided lens redshifts are known.

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

This paper investigates the use of strongly lensed gravitational-wave signals from massive binary black hole mergers to measure the Hubble constant with future space-based detectors such as Taiji and LISA. It examines two cases: one where the source redshift is unknown and one where it is independently measured via electromagnetic observations. The work shows that useful constraints on H0 remain possible in the unknown-source-redshift case as long as the lens redshift is known. Joint Taiji plus LISA data improves the precision on individual events by roughly a factor of two relative to Taiji alone, and stacking five simulated events tightens the 95 percent credible interval on H0 to 0.11 without source redshift and to 0.042 with it.

Core claim

By simulating strongly lensed gravitational-wave events from massive binary black hole mergers and performing Bayesian inference on the Hubble constant, the analysis establishes that joint Taiji and LISA observations improve H0 measurement precision by a factor of approximately two over Taiji alone for single events; combining five such events produces a 95 percent credible interval on H0 of 1.1 times 10 to the minus 1 when source redshift is unknown and 4.2 times 10 to the minus 2 when source redshift is known, assuming the lens redshift is available.

What carries the argument

Bayesian inference applied to time-delayed signals from strongly lensed binary black hole mergers recorded by space-based gravitational-wave detector networks, using known lens redshifts to break distance-redshift degeneracies.

If this is right

  • Meaningful constraints on H0 can still be achieved without source-redshift information provided the lens redshift is known.
  • The joint Taiji plus LISA analysis improves the measurement precision of H0 by approximately a factor of two compared with the Taiji-only configuration for individual events.
  • Combining five simulated SLGW events yields an uncertainty in H0, quantified by the 95 percent credible interval, of 1.1 times 10 to the minus 1 when source redshift is treated as unknown and 4.2 times 10 to the minus 2 when source redshift is independently measured.

Where Pith is reading between the lines

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

  • This method supplies an independent distance ladder that could be cross-checked against supernova or CMB determinations of H0 to test for systematic offsets.
  • Adding electromagnetic identification of source redshifts for even a subset of events would tighten the combined constraint below the 4 percent level shown for five events.
  • Networks of space-based detectors appear necessary to reach the quoted population-level precisions, implying that single-detector data alone would remain limited even with many events.

Load-bearing premise

The quoted precisions hold only if binary black hole merger rates, strong-lensing statistics, detector noise properties, and lens redshift measurements are all known accurately in advance.

What would settle it

Detection and analysis of five real SLGW events with known lens redshifts that produce a 95 percent credible interval on H0 wider than 0.11 when source redshifts are unavailable would show the claimed precision cannot be reached.

read the original abstract

The measurement of the Hubble constant $H_0$ plays a central role in modern cosmology. In this work, we investigate the potential of strongly lensed gravitational-wave (SLGW) signals from massive binary black hole mergers to constrain $H_0$ using future space-based detector networks. We consider two observational scenarios: one in which the source redshift is unknown, and another in which it is independently determined through electromagnetic observations. We show that meaningful constraints on $H_0$ can still be achieved without source-redshift information, provided that the lens redshift is known. For individual SLGW events, the joint Taiji+LISA analysis improves the measurement precision of $H_0$ by approximately a factor of two compared with the Taiji-only configuration. Extending the analysis to the population level, we combine five simulated SLGW events and find that the uncertainty in $H_0$, quantified by the 95\% credible interval, reaches the $1.1\times10^{-1}$ level when the source redshift is treated as unknown, and further improves to $4.2\times10^{-2}$ when the source redshift is independently measured. Our results demonstrate that joint space-based gravitational-wave observations can substantially enhance the cosmological capability of SLGW events and provide a promising avenue for precision measurements of the Hubble constant.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper forecasts constraints on the Hubble constant H0 from strongly lensed gravitational-wave events produced by massive binary black hole mergers, observed with future space-based detector networks (Taiji and LISA). It considers two cases (source redshift unknown vs. independently measured) and reports that meaningful H0 constraints remain possible when only the lens redshift is known; joint Taiji+LISA observations improve single-event precision by a factor of approximately two relative to Taiji alone; and a population of five simulated events yields 95% credible intervals of 1.1×10^{-1} (source z unknown) and 4.2×10^{-2} (source z measured).

Significance. If the quoted credible intervals are robust, the work demonstrates a concrete pathway for cosmological inference from SLGWs that does not require electromagnetic source redshifts, thereby expanding the science case for space-based GW networks. The explicit comparison of single-detector versus network performance and the population-level combination of five events constitute useful benchmark forecasts for the field.

major comments (3)
  1. [§4] §4 (population-level results): The reported 95% credible intervals (1.1×10^{-1} and 4.2×10^{-2}) are obtained from Monte Carlo simulations that fix the BBH merger-rate density, strong-lensing optical depth, and detector PSDs without marginalizing over plausible variations in these inputs; because both the expected number of detectable events and the information per event scale directly with these quantities, the quoted precisions are conditional on the specific background model rather than marginal forecasts.
  2. [Methods] Methods section (simulation and likelihood construction): The abstract and results present credible intervals but supply no explicit description of the statistical model, error propagation, or validation tests for the lensing magnification, time-delay, and detector-response assumptions; without this information it is not possible to assess whether the reported intervals correctly propagate the joint uncertainties in GW parameters and lensing geometry.
  3. [§3.2] §3.2 (single-event analysis): The claim that the joint Taiji+LISA configuration improves H0 precision by a factor of two is presented without an accompanying table or figure that isolates the contribution of each detector network to the posterior width, making it impossible to verify the factor-of-two improvement or to assess its dependence on the assumed lens-redshift precision.
minor comments (2)
  1. Notation for the 95% credible interval is used inconsistently between the abstract and the main text; a single, clearly defined symbol would improve readability.
  2. The manuscript would benefit from an explicit statement of the assumed lens-redshift measurement uncertainty (e.g., spectroscopic precision) in the simulation setup.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the scope and presentation of our forecasting results. We address each major comment below.

read point-by-point responses

  1. Referee: [§4] §4 (population-level results): The reported 95% credible intervals (1.1×10^{-1} and 4.2×10^{-2}) are obtained from Monte Carlo simulations that fix the BBH merger-rate density, strong-lensing optical depth, and detector PSDs without marginalizing over plausible variations in these inputs; because both the expected number of detectable events and the information per event scale directly with these quantities, the quoted precisions are conditional on the specific background model rather than marginal forecasts.

    Authors: We agree that the quoted credible intervals are conditional on the fixed values chosen for the merger-rate density, lensing optical depth, and detector PSDs. Such conditional forecasts are standard in the literature to establish benchmark performance. We will revise the text in §4 to state this conditionality explicitly and add a short discussion of how plausible variations in these inputs would affect the reported precisions. revision: yes

  2. Referee: [Methods] Methods section (simulation and likelihood construction): The abstract and results present credible intervals but supply no explicit description of the statistical model, error propagation, or validation tests for the lensing magnification, time-delay, and detector-response assumptions; without this information it is not possible to assess whether the reported intervals correctly propagate the joint uncertainties in GW parameters and lensing geometry.

    Authors: The Methods section provides the overall simulation framework and likelihood construction, but we acknowledge that additional detail on the statistical model, error propagation, and validation would improve transparency. We will expand the Methods section with explicit descriptions of these elements, including how joint uncertainties in GW parameters and lensing geometry are propagated. revision: yes

  3. Referee: [§3.2] §3.2 (single-event analysis): The claim that the joint Taiji+LISA configuration improves H0 precision by a factor of two is presented without an accompanying table or figure that isolates the contribution of each detector network to the posterior width, making it impossible to verify the factor-of-two improvement or to assess its dependence on the assumed lens-redshift precision.

    Authors: We will add a table (or supplementary figure) in §3.2 that reports the 95% credible interval widths for Taiji-only, LISA-only, and joint configurations, thereby isolating the network contribution and showing its dependence on lens-redshift precision. revision: yes

Circularity Check

0 steps flagged

No circularity: H0 constraints are forward-simulation outputs

full rationale

The paper reports H0 credible intervals obtained by running Monte Carlo simulations of SLGW events under fixed assumptions for merger rates, lensing statistics, detector noise, and lens redshifts, then sampling only the GW and lensing parameters. These outputs do not reduce by construction to any fitted input or self-citation chain; the quoted precisions (1.1e-1 and 4.2e-2) are direct numerical results of the chosen forward model rather than tautological re-expressions of its inputs. No self-definitional, fitted-prediction, or uniqueness-imported steps appear in the abstract or described methodology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on standard domain assumptions about merger populations and lensing; no explicit free parameters or invented entities are stated. Full paper would be needed to enumerate simulation choices.

axioms (1)
  • domain assumption Standard models for binary black hole merger rates and strong-lensing optical depth are sufficient to generate realistic event populations
    The quoted constraints are derived from simulated populations whose generation is not described.

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Reference graph

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