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arxiv: 2606.24278 · v1 · pith:5WK7NLPJnew · submitted 2026-06-23 · 🌌 astro-ph.CO

Extragalactic test of General Relativity with time-delay gravitational lenses

Wuzheng Guo , Shuo Cao , Qiumin Wang , Yun Chen , Marek Biesiada , Tonghua Liu , Yujie Lian This is my paper

Pith reviewed 2026-06-25 23:31 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords strong gravitational lensingtime-delay distancepost-Newtonian parameterBAO measurementsGaussian process regressiongeneral relativity testsound horizonH0LiCOW
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The pith

Time-delay gravitational lenses combined with BAO-reconstructed distances give γ_PPN = 0.93^{+0.16}_{-0.17} consistent with general relativity.

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

The paper reconstructs angular diameter distances from DESI DR2 BAO data using Gaussian process regression and combines them with time-delay observations from four H0LiCOW strong lensing systems to estimate the post-Newtonian parameter γ_PPN. It performs the first simultaneous extraction of γ_PPN and the sound horizon scale r_d without assuming any cosmological model or gravity theory. A sympathetic reader cares because this supplies a direct, low-assumption test of general relativity on extragalactic scales where alternative gravity models could produce detectable differences. In a distance-ratio framework that removes r_d dependence, the γ_PPN bound tightens further while remaining consistent with the GR value of 1 within 1σ.

Core claim

Using Gaussian Process regression on DESI DR2 BAO measurements to reconstruct angular diameter distances and applying them to time-delay data from four H0LiCOW lenses, the analysis yields γ_PPN = 0.93^{+0.16}_{-0.17} and r_d = 136.36^{+5.14}_{-3.20} Mpc. This is presented as the first simultaneous measurement of these quantities without assumptions on the contents of the universe or the theory of gravity. In the new distance-ratio framework D_Δt/D_l that avoids bias from r_d, the γ_PPN constraint improves to 0.89^{+0.19}_{-0.15}. The results constitute a direct test of GR at extragalactic scales and agree with the GR prediction within 1σ.

What carries the argument

The time-delay distance in the parameterized post-Newtonian framework, which relates observed image delays in strong lenses to angular diameter distances via the parameter γ_PPN that governs light deflection.

If this is right

  • The measured γ_PPN near 1 supports general relativity on extragalactic scales without cosmological priors.
  • The sound horizon scale r_d can be extracted at the same time as the gravity parameter.
  • Switching to the distance ratio D_Δt/D_l removes dependence on r_d and tightens the γ_PPN bound.
  • The method enables model-independent tests of gravity using existing and future strong-lensing samples.

Where Pith is reading between the lines

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

  • Adding more time-delay lenses from upcoming surveys could shrink the uncertainty on γ_PPN enough to probe small departures from GR.
  • The extracted r_d value supplies an independent anchor for early-universe calculations that can be cross-checked against CMB or other BAO analyses.
  • The same reconstructed distances could be applied to other lensing observables to test consistency across different gravity-sensitive quantities.

Load-bearing premise

The parameterized post-Newtonian time-delay distance formula accurately reproduces the observed delays in the H0LiCOW systems once the angular diameter distances are supplied, with no large unmodeled systematics from lens mass distributions or source structure.

What would settle it

Future independent distance reconstructions or additional time-delay lens systems that produce a γ_PPN value lying outside the reported 1σ interval around 0.93 would indicate either unaccounted systematics or a deviation from general relativity.

read the original abstract

Strong gravitational lensing, a key prediction of General Relativity (GR), offers a unique environment for examining alternative modified gravity theories. In this Letter, we employ a model-independent approach to estimate the parameterized post-Newtonian parameter $\gamma_{\rm PPN}$ using the time-delay measurements from H0LiCOW strong lensing systems. To minimize potential biases from cosmological models in testing GR, we use Gaussian Process regression (GPR) to reconstruct angular diameter distances ($D_{\rm A}$) from the newest baryon acoustic oscillation (BAO) measurements, provided by the Dark Energy Spectroscopic Instrument (DESI) DR2 data. Based on the reconstructed angular diameter distances and four H0LiCOW lenses, we directly estimate the post-Newtonian parameter $\gamma_{\rm PPN}=0.93^{+0.16}_{-0.17}$ and the sound horizon scale $r_{\rm d}=136.36^{+5.14}_{-3.20}~{\rm Mpc}$. This is the first simultaneous measurement of $\gamma_{\rm PPN}$ and $r_{\rm d}$ without any assumptions about the contents of the universe or the theory of gravity. In the new framework of distance ratio $D_{\Delta t}/D_{\rm l}$ which avoids the bias introduced by $r_{\rm d}$, the $\gamma_{\rm PPN}$ constraint can be further improved to $\gamma_{\rm PPN}=0.89^{+0.19}_{-0.15}$. Our results provide a direct test of GR at the extragalactic scale, which is well consistent with the prediction of GR within $1\sigma$.

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 uses Gaussian Process regression on DESI DR2 BAO data to reconstruct angular diameter distances D_A(z) in a nonparametric way, then combines these with published time-delay distances D_Δt from four H0LiCOW systems to simultaneously constrain the post-Newtonian parameter γ_PPN and sound horizon r_d, reporting γ_PPN = 0.93^{+0.16}_{-0.17} (consistent with GR within 1σ) and r_d = 136.36^{+5.14}_{-3.20} Mpc; an alternative distance-ratio framework D_Δt/D_l yields a similar γ_PPN constraint. The central claim is that this constitutes the first such measurement without assumptions on cosmic contents or gravity theory.

Significance. If the central result holds after addressing data-consistency issues, the nonparametric GPR approach and joint fit for γ_PPN and r_d would constitute a genuine model-independent extragalactic test of GR, with the simultaneous r_d constraint and the distance-ratio variant as notable technical strengths.

major comments (2)
  1. [Methodology section describing combination of H0LiCOW data] Methodology section describing combination of H0LiCOW data: The published H0LiCOW D_Δt values are obtained by modeling image positions and Fermat potentials Δφ under standard GR (deflection angle = 4GM/b). In the PPN framework the deflection scales as (1+γ_PPN)/2, which modifies both the lens equation (hence inferred Δφ and mass parameters) and the Shapiro-delay term. Inserting GR-derived D_Δt directly into the PPN distance formula therefore mixes inconsistent assumptions; this is load-bearing for the claim of testing GR 'without any assumptions about ... the theory of gravity' and must be resolved by re-deriving the lens models with free γ_PPN or by explicit justification.
  2. [Section on GPR reconstruction and joint fit] Section on GPR reconstruction and joint fit: The manuscript does not provide the specific GPR kernel, hyperparameter priors, or full covariance treatment between the reconstructed D_A(z) and the H0LiCOW D_Δt uncertainties. Without these details or robustness tests to reasonable variations, it is unclear whether the reported γ_PPN and r_d posteriors are stable; this directly affects the soundness of the central simultaneous measurement.
minor comments (2)
  1. [Abstract] The abstract refers to 'the new framework of distance ratio D_Δt/D_l' but does not define D_l; add an explicit definition or equation reference in the main text.
  2. Figure captions and text should clarify how the GPR-reconstructed D_A(z) uncertainties are propagated into the joint posterior for γ_PPN and r_d.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments. We address each major comment below and plan to revise the manuscript to incorporate clarifications and additional details.

read point-by-point responses

  1. Referee: Methodology section describing combination of H0LiCOW data: The published H0LiCOW D_Δt values are obtained by modeling image positions and Fermat potentials Δφ under standard GR (deflection angle = 4GM/b). In the PPN framework the deflection scales as (1+γ_PPN)/2, which modifies both the lens equation (hence inferred Δφ and mass parameters) and the Shapiro-delay term. Inserting GR-derived D_Δt directly into the PPN distance formula therefore mixes inconsistent assumptions; this is load-bearing for the claim of testing GR 'without any assumptions about ... the theory of gravity' and must be resolved by re-deriving the lens models with free γ_PPN or by explicit justification.

    Authors: We acknowledge this important point regarding the consistency of assumptions. The H0LiCOW D_Δt are derived under GR, and using them in a PPN context introduces a potential inconsistency. Since our best-fit γ_PPN is close to unity, the induced bias is expected to be small (second-order in (γ_PPN - 1)). We will revise the manuscript to include an explicit discussion of this approximation, quantify the possible systematic effect, and qualify our claim of being assumption-free on gravity theory. A complete re-derivation of the lens models allowing for free γ_PPN is computationally intensive and left for future work, but we believe the current approach remains a useful first step. revision: partial

  2. Referee: Section on GPR reconstruction and joint fit: The manuscript does not provide the specific GPR kernel, hyperparameter priors, or full covariance treatment between the reconstructed D_A(z) and the H0LiCOW D_Δt uncertainties. Without these details or robustness tests to reasonable variations, it is unclear whether the reported γ_PPN and r_d posteriors are stable; this directly affects the soundness of the central simultaneous measurement.

    Authors: We thank the referee for pointing out the lack of these technical specifications. In the revised version, we will add a dedicated subsection detailing the GPR kernel (squared exponential with specific length-scale and variance priors), the hyperparameter optimization procedure, and how the covariance between the GPR-reconstructed D_A(z) and the H0LiCOW uncertainties is handled in the likelihood. We will also include robustness checks by varying the kernel hyperparameters and reporting the resulting variations in the γ_PPN and r_d constraints. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in external data

full rationale

The paper reconstructs angular diameter distances via nonparametric GPR from DESI DR2 BAO measurements and combines them with published H0LiCOW time-delay distances to jointly constrain γ_PPN and r_d. No equation or step reduces by construction to a fitted parameter renamed as a prediction, nor does any load-bearing premise rest on a self-citation chain. The central result therefore retains independent empirical content from the input datasets.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The measurement rests on the applicability of the PPN time-delay formula to real lens systems and on the fidelity of the nonparametric distance reconstruction from BAO; no new entities are introduced.

free parameters (2)
  • γ_PPN = 0.93
    Parameterized post-Newtonian parameter estimated from the combined data.
  • r_d = 136.36 Mpc
    Sound horizon scale estimated simultaneously from the same data combination.
axioms (2)
  • domain assumption The parameterized post-Newtonian time-delay distance formula holds for the H0LiCOW systems once angular diameter distances are provided.
    Invoked to convert observed time delays into a constraint on γ_PPN.
  • domain assumption Gaussian Process regression with the chosen kernel accurately reconstructs angular diameter distances from the DESI DR2 BAO measurements without introducing systematic bias.
    Required for the model-independent distance input to the lensing analysis.

pith-pipeline@v0.9.1-grok · 5846 in / 1548 out tokens · 29573 ms · 2026-06-25T23:31:22.060242+00:00 · methodology

discussion (0)

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