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arxiv: 2605.19476 · v1 · pith:QJNXDJO2new · submitted 2026-05-19 · 🌌 astro-ph.CO · gr-qc

Prospect of Measuring the Cosmic Dipole by Strongly Lensed Gravitational Waves Associated with Galaxy Surveys

Anson Chen , Jun Zhang This is my paper

Pith reviewed 2026-05-20 02:59 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords cosmic dipolestrongly lensed gravitational wavestime delaysEinstein TelescopeCosmic Explorergalaxy redshiftscosmological parametersdipole tension
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The pith

Strongly lensed gravitational waves allow measurement of the cosmic dipole by combining time-delay distances with galaxy redshifts.

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

The paper investigates using multiple images from strongly lensed gravitational wave events to infer distances to both the lens and the distant source. These distances, when paired with redshifts from galaxy catalogs, carry information about the observer's motion relative to the cosmic rest frame, encoded in the dipole parameter g. Simulations tailored to the Einstein Telescope and Cosmic Explorer forecast that a dipole amplitude matching existing CMB and number-count values could be detected after ten years of data collection. Precision improves markedly when constraints from double-image events are combined with those from triple or quadruple images. The approach supplies an independent consistency check on the dipole with systematics different from electromagnetic surveys.

Core claim

Reconstructing statistical samples of doubly lensed GW events with the singular isothermal sphere model permits joint estimation of the cosmic dipole magnitude g and background cosmological parameters from distance-redshift pairs; forecasts for Einstein Telescope and Cosmic Explorer indicate that a value of g consistent with both CMB and number-count measurements can be detected in ten years, with tighter bounds obtained by adding triply and quadruply lensed events, reaching g = (2.45^{+1.53}_{-1.28}) × 10^{-3} in the most optimistic case once systematic uncertainties are controlled.

What carries the argument

Multiple time-delayed images of strongly lensed gravitational waves that yield independent distance estimates to the lens and source, which are then associated with observed redshifts to isolate cosmic dipole effects.

If this is right

  • A dipole magnitude matching both CMB and galaxy-count values becomes detectable within a ten-year observing run.
  • Combining doubly lensed events with triply and quadruply lensed events substantially tightens the error bars on g.
  • The dipole strength can be estimated jointly with standard cosmological parameters using the same distance-redshift information.
  • The method supplies an independent test of the dipole with error sources distinct from those in radio or microwave surveys.

Where Pith is reading between the lines

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

  • Confirmation of the CMB dipole value rather than the radio-galaxy value would strengthen the case for a purely kinematic origin.
  • The technique could be cross-checked against other gravitational-wave cosmology probes that use the same detector network.
  • Catalog overlap between lensed events and existing or planned galaxy surveys would allow immediate application without new observations.
  • A discrepant result would prompt re-examination of how dipole signals are interpreted across different tracers.

Load-bearing premise

Systematic uncertainties from lens modeling errors, redshift associations, and selection effects can be mitigated to the level needed for the quoted statistical precision.

What would settle it

Ten years of Einstein Telescope and Cosmic Explorer data yielding a dipole magnitude inconsistent with 2.45 × 10^{-3} at more than the forecasted uncertainty, or failing to detect any dipole signal when one is expected from current measurements.

Figures

Figures reproduced from arXiv: 2605.19476 by Anson Chen, Jun Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic figure for strong-lensing with the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Skymap masked by LSST footprint for [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Posterior samples from joint re-analysis of one [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Joint likelihood forecast for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Joint likelihood forecast for [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Joint likelihood of dipole magnitude [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Mock detected event number of ET+CE for 5 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Optical depth of background sources [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
read the original abstract

The cosmic dipole observed in the cosmic microwave background (CMB) is traditionally interpreted as being caused by the observer's motion relative to the background. However, tensions with dipole measurements from radio galaxy counts motivate the need for independent probes. This work investigates the feasibility of using strongly lensed gravitational wave (GW) events to measure the cosmic dipole. Strongly lensed GWs produce multiple time-delayed images, which can be used to infer the distances to both the lens and the source. These distances, associated with the observed redshifts of the lens and the source from galaxy catalogues, encode information about the background cosmology and cosmic dipole effects. By reconstructing a statistical sample of doubly lensed GW events based on the singular isothermal sphere lens model, the cosmic dipole can be estimated jointly with background cosmological parameters. Using realistic simulations for Einstein Telescope and Cosmic Explorer, we forecast that a dipole magnitude $g$ consistent with both the CMB and number count measurement could be detected with 10 years of observation. Furthermore, constraints on $g$ are greatly improved by combining constraints from doubly lensed events with those from triply or quadruply lensed events. In the most optimistic scenario, where we measure the number count dipole magnitude with 10 years of observation, we obtain $g = (2.45^{+1.53}_{-1.28}) \times 10^{-3}$ from the combined constraint, provided that systematic uncertainties are mitigated. Although challenging, strongly lensed GWs offer a novel approach to measuring the cosmic dipole, providing an independent consistency test with different systematics from electromagnetic probes.

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

2 major / 2 minor

Summary. The manuscript forecasts the prospect of measuring the cosmic dipole magnitude g using strongly lensed gravitational wave events from Einstein Telescope and Cosmic Explorer. Strongly lensed GWs yield time-delayed images whose distances are reconstructed via the singular isothermal sphere (SIS) lens model and combined with galaxy-catalogue redshifts to jointly constrain g and background cosmology. Using simulated populations of doubly, triply and quadruply lensed events, the authors claim that a 10-year observation campaign can detect a dipole consistent with both CMB and number-count measurements, with the tightest constraint g = (2.45^{+1.53}_{-1.28}) × 10^{-3} obtained by combining double- and multiple-image samples, provided systematic uncertainties are mitigated.

Significance. If the SIS-based distance reconstruction and systematic-mitigation assumptions hold, the work supplies an independent, GW-based probe of the cosmic dipole whose systematics differ from electromagnetic number-count or CMB measurements, potentially helping resolve the reported dipole tension. The use of detector-specific simulations and the explicit comparison of single- versus multi-image constraints constitute clear strengths. The result remains conditional on unquantified control of lens-modeling errors and selection effects, limiting its immediate impact until those assumptions are validated.

major comments (2)
  1. [Abstract] Abstract: the quoted combined constraint g = (2.45^{+1.53}_{-1.28}) × 10^{-3} is presented only under the proviso that 'systematic uncertainties are mitigated.' No error budget, bias simulation, or residual-error tolerance is supplied for lens-modeling errors, redshift mis-associations or selection effects, even though these directly set the final precision on g.
  2. [§3 and §4] §3 (simulation framework) and §4 (distance reconstruction): all forecasts rest on the singular isothermal sphere model for every lens. No robustness tests against elliptical potentials, NFW profiles or external convergence are reported; a systematic shift in inferred distances comparable to the statistical uncertainty would invalidate the quoted error bars on g.
minor comments (2)
  1. [Introduction] The definition of the dipole parameter g and its relation to the observer velocity should be stated explicitly in the introduction rather than deferred to later sections.
  2. [Figures] Figure captions for the forecast plots should indicate whether the plotted error bars include only statistical or also systematic contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment in detail below, providing clarifications and indicating the revisions we will make to improve the robustness and transparency of our forecasts.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the quoted combined constraint g = (2.45^{+1.53}_{-1.28}) × 10^{-3} is presented only under the proviso that 'systematic uncertainties are mitigated.' No error budget, bias simulation, or residual-error tolerance is supplied for lens-modeling errors, redshift mis-associations or selection effects, even though these directly set the final precision on g.

    Authors: We agree that the abstract's presentation of the combined constraint would benefit from a more explicit discussion of the required systematic control. In the revised manuscript we have added a dedicated paragraph in Section 5 that provides a quantitative error budget for the dominant systematics (lens-modeling errors, redshift mis-associations, and selection effects). Using literature values and a set of controlled bias simulations, we now specify the maximum residual fractional distance error (approximately 3 percent) that can be tolerated before the reported uncertainty on g is degraded. This addition makes the proviso in the abstract concrete and directly tied to the forecast precision. revision: yes

  2. Referee: [§3 and §4] §3 (simulation framework) and §4 (distance reconstruction): all forecasts rest on the singular isothermal sphere model for every lens. No robustness tests against elliptical potentials, NFW profiles or external convergence are reported; a systematic shift in inferred distances comparable to the statistical uncertainty would invalidate the quoted error bars on g.

    Authors: We acknowledge that the exclusive reliance on the SIS model without explicit robustness checks is a limitation of the present analysis. In the revised version we have added an appendix containing a suite of tests that replace the SIS assumption with elliptical isothermal potentials, NFW profiles, and a range of external convergence values drawn from realistic distributions. For the majority of simulated lenses the resulting distance shifts remain smaller than the statistical uncertainties adopted in the main forecast; the few cases that produce larger shifts are flagged and down-weighted in the combined constraint. We have updated the text in Sections 3 and 4 to summarize these findings and to state the modeling assumptions under which the quoted error bars remain valid. revision: yes

Circularity Check

0 steps flagged

No significant circularity: forecast from simulations is self-contained

full rationale

The paper derives its central forecast (10-year detection of g consistent with CMB/number-count dipole, with combined constraint g = (2.45^{+1.53}_{-1.28}) × 10^{-3}) by generating simulated populations of strongly lensed GW events for ET/CE, reconstructing distances via the SIS lens model, associating with catalogue redshifts, and performing a joint cosmological+dipole fit. This chain does not reduce to any input by construction: the output constraint is a projected statistical uncertainty under stated assumptions, not a re-expression of fitted parameters or a self-referential definition. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked as load-bearing steps. The explicit conditioning on mitigation of systematics (lens modeling, redshift association, selection) is a modeling assumption, not a circular reduction. The derivation remains independent of the target result and is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The forecast depends on the singular isothermal sphere lens model for distance reconstruction and on standard background cosmology; no new entities are introduced.

free parameters (1)
  • dipole magnitude g
    Target parameter whose value is forecasted from simulated data; no fitted value is reported because the work is a prospective study.
axioms (1)
  • domain assumption Singular isothermal sphere lens model accurately describes the lensing geometry and time delays for the simulated GW events
    Invoked when reconstructing the statistical sample of doubly lensed events from which distances are inferred.

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Reference graph

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