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REVIEW 3 major objections 4 minor 78 references

Combining strong-lensing distance ratios with DESI-DR2 baryon acoustic oscillations and three supernova compilations yields a model-independent cosmographic measurement in which the universe stays flat and accelerating.

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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2026-08-04 00:27 UTC pith:7UG5SA3W

load-bearing objection Useful extension of the DSR/SGL/SNe cosmography framework to DESI-DR2, but the abstract's flatness-at-68% claim is contradicted by the paper's own Table 3. the 3 major comments →

arxiv 2511.00789 v2 pith:7UG5SA3W submitted 2025-11-02 astro-ph.CO

A cosmographic analysis using DESI-DR2 and strong lensing: II. Distance Ratio measurements

Darshan Kumar (HNAS) , Deepak Jain (DU) , Shobhit Mahajan (DU) This is my paper
classification astro-ph.CO
keywords gravitational lensingdistance sum rulecosmographyspatial curvaturebaryon acoustic oscillationsType Ia supernovaeDESIcosmic acceleration
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 tries to measure cosmic geometry and expansion history without assuming a dark-energy model. It combines distance ratios from 161 strong gravitational lens systems with three Type Ia supernova samples and DESI-DR2 baryon acoustic oscillation data, using a fourth-order Taylor expansion in y=z/(1+z) and the distance sum rule. The central result is that all dataset combinations remain consistent with a flat, accelerating universe: the deceleration parameter is negative, the jerk parameter is near the value 1 predicted by standard cosmology, and spatial curvature is consistent with zero in every combination, with flatness supported at the 95% level once DESI-DR2 is included. Adding the DESI-DR2 data sharply reduces parameter uncertainties and brings the inferred Hubble constant close to the Planck value. A sympathetic reader would care because the test is model-independent and uses lensing geometry rather than distance-ladder calibration.

Core claim

Using a sample of 161 galaxy-scale strong lenses, the paper derives distance-ratio measurements and applies the distance sum rule to obtain a direct, model-independent constraint on the spatial curvature parameter Ωk0, along with the deceleration q0, jerk j0, and snap s0 parameters from a fourth-order cosmographic expansion in y=z/(1+z). For each of the three supernova compilations, the joint analysis keeps flat geometry viable; for example, with PantheonPlus alone Ωk0=0.049±0.08, q0=-0.472±0.07, j0=0.77±0.72, and with DESI-DR2 added H0=67.86±0.45 km/s/Mpc, Ωk0=0.139±0.06, q0=-0.481±0.06, j0=1.16±0.41. The paper concludes that the data are consistent with a flat ΛCDM-like expansion, that cos

What carries the argument

The load-bearing element is the distance sum rule (DSR), a geometric identity in the FLRW metric that links the comoving distances from observer to lens, observer to source, and lens to source, and can be rewritten as the distance ratio d_ls/d_os probed by strong lensing. The ratio is computed from each lens's Einstein radius under a Singular Isothermal Sphere mass model, then compared with the same ratio built from the fourth-order Taylor expansion of the Hubble parameter in y=z/(1+z). The DSR is what turns lensing observations into a direct measurement of Ωk0, while the y-expansion supplies q0, j0, and s0 without fixing a background cosmology.

Load-bearing premise

The fourth-order Taylor expansion of the Hubble parameter in y = z/(1+z) is assumed accurate for all lens systems, including those with source redshift up to about 3.6, so any error from the omitted higher-order terms must be small compared with the data uncertainties.

What would settle it

Compare the distance-ratio predictions of the fourth-order cosmographic expansion against exact distances in a flat ΛCDM model at the highest source redshifts in the sample; if the difference is comparable to or larger than the reported observational uncertainties, the inferred curvature and deceleration parameters are biased and the consistency claim would not survive.

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

If this is right

  • Flat spatial geometry remains viable at the 95% confidence level for every supernova combination, and at 68% confidence once DESI-DR2 data are included.
  • The deceleration parameter is consistently negative, so cosmic acceleration is detected without assuming a dark-energy model.
  • The jerk parameter is consistent with the ΛCDM value j0=1 in all cases, with the tightest constraint near 1.16±0.41.
  • Adding DESI-DR2 reduces parameter uncertainties by a factor of several and moves the inferred Hubble constant (about 66.7–68.7 km/s/Mpc) close to the Planck value.
  • The snap parameter s0 remains too weakly constrained to test higher-order expansion dynamics, though DESI-DR2 noticeably narrows its uncertainty.

Where Pith is reading between the lines

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

  • The main risk I see is truncation of the fourth-order y-expansion: with sources out to z_s≈3.6, the neglected fifth-order term could be comparable in size to the current Ωk0 uncertainty, and computing it from the paper's distance formulas would settle whether the flatness conclusion is an artifact of the expansion.
  • The companion time-delay analysis reportedly shifts curvature in the opposite direction when DESI-DR2 is added; if both results hold, distance ratios and time delays trace different degeneracies, and combining them could break the curvature–expansion degeneracy more cleanly than either probe alone.
  • A natural next test is applying the same DSR machinery to future wide-field lens surveys with thousands of systems; the poorly constrained snap parameter should tighten fastest, since higher-order terms become statistically accessible with larger samples.

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. This manuscript (Paper II of a two-part series) presents a cosmographic analysis combining 161 galaxy-scale strong-lensing distance ratios with three Type Ia supernova compilations (PantheonPlus, Union3, DESY5) and DESI DR2 BAO data. The authors expand the Hubble parameter to fourth order in y = z/(1+z), use the distance sum rule to constrain the spatial curvature parameter Ωk0, and sample (Ωk0, q0, j0, s0) with MCMC. The paper reports that SGL+SN data are consistent with flatness at 95% CL, that adding DESI DR2 tightens constraints, and that the abstract summarizes this as preserving agreement with flat geometry at 68% CL. The main results appear in Tables 2 and 3.

Significance. If correct, the analysis provides a useful model-independent cross-check of spatial curvature and cosmographic parameters using the distance sum rule with SGL distance ratios, complementing time-delay cosmography. The inclusion of three independent SN samples and the current DESI DR2 BAO dataset, with full covariance information, is a strength. The paper also explicitly uses a model-independent cosmographic framework and provides MCMC-based posteriors. However, the central summary claim about flatness at 68% is contradicted by the paper's own Table 3, and the expansion-truncation error and reliance on deferred formulas from Paper I are unresolved, so the quantitative conclusions are not yet fully supported.

major comments (3)
  1. [Abstract; §3.2; Table 3] The abstract and Section 3.2 state that including DESI-DR2 'preserves agreement with flat geometry at the 68% confidence level.' The 68% credible intervals in Table 3 exclude Ωk0=0 for all three DESI-DR2 combinations: SGL+PantheonPlus+DESI gives Ωk0=0.139+0.061−0.058 (interval [0.081, 0.200]); SGL+Union3+DESI gives 0.132+0.066−0.062 (interval [0.070, 0.198]); SGL+DESY5+DESI gives −0.054+0.050−0.046 (interval [−0.100, −0.004]). Thus flatness is excluded at 68% CL for every combination, and only excluded/consistent at 95% CL in the text. The headline conclusion must be corrected to say 95% CL, or the analysis must be checked for a systematic bias producing this offset.
  2. [§2.3, Eq. (2.7)] The cosmographic expansion is truncated at fourth order in y, but the lens sample reaches source redshifts z_s up to 3.595, i.e. y ≈ 0.78. No estimate of the truncation error is given, and the actual distance expansions used to compute D_ol and D_os are deferred to 'Paper I.' A fourth-order Taylor series around y=0 can be inaccurate at y=0.78, and a systematic truncation bias would shift all derived parameters, in particular Ωk0. Please provide the explicit expansion formulas in an appendix or cite the previous paper with an arXiv number, and quantify the truncation error (e.g., by comparing the fourth-order result to an exact ΛCDM distance at the best-fit parameters, or by including a fifth-order term).
  3. [§2.3] The analysis relies on unpublished or vague references to 'Paper I' for core ingredients: the distance expansions in y, the SNIa magnitude-marginalization formula leading to Eq. (2.15), and the BAO distance definitions. As a standalone JCAP submission, the reader cannot reproduce the analysis without these formulas and references. Please include the necessary expressions in this paper or explicitly cite the companion paper with an arXiv identifier, and state the relation between the two papers' notation.
minor comments (4)
  1. [§3.3; Figure 4] Figure 4 is referenced in Section 4 as a 'tension matrix,' but the figure is not described in the text, no definition of the quantity plotted is given, and the units/sigma calculation is unspecified. Please add a caption and a sentence describing how the tension is computed.
  2. [§3.1/§3.2] Table 2 does not report H0 although H0 is mentioned in the text ('inferred values of H0 tend to exceed those predicted by Planck'). Either report H0 in Table 2 for completeness or remove the statement.
  3. [§2.2] The BAO analysis applies a Gaussian prior on r_d from Ref. [62], but the text does not give the prior's central value and width. Please state the prior explicitly.
  4. [§2.3] There is a typo in Section 2.3: '12 walkers, each running for 10,000 steps to to achieve' — duplicated 'to.'

Circularity Check

0 steps flagged

No significant circularity: the fitted parameters are not by construction equal to any predicted quantity; repeated deferral to Paper I and an internal 68% flatness inconsistency are correctness/reproducibility issues, not circular reductions.

full rationale

The paper's derivation chain is a standard likelihood fit: Eqs. (2.5)-(2.10) define the cosmographic series and the distance sum rule, and Eqs. (2.11)-(2.17) minimize chi-squares against external SGL, SNIa, and DESI-DR2 data. No parameter is defined in terms of a target result, and no fitted quantity is later relabeled as an independent prediction; the SGL distance ratios, SNIa magnitudes, and DESI BAO observables enter as separate external datasets. The DSR expression for d_AR is an exact FLRW geometric identity rather than an ansatz that presupposes the fitted Omega_k0. The paper does defer important technical content to the authors' own Paper I ('For details on the expansions and their application, we refer the reader to paper I'; 'For a detailed derivation and discussion of the marginalization procedure, we refer the reader to Paper I'), and the abstract's claim that DESI-DR2 preserves agreement with flat geometry at 68% is contradicted by Table 3's 68% intervals (e.g., Omega_k0 = 0.139+0.061-0.058 excludes zero). However, these are omitted-derivation/reproducibility and internal-consistency/correctness concerns, not cases where a result reduces to its own input. The fourth-order y-expansion truncation at z_s ~ 3.6 is likewise a possible systematic bias, not a circularity. No specific reduction of the kind required for a circularity finding is exhibited, so the circularity score is minimal.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The paper introduces no new physical entities. Its central fit has six free parameters (H0, Omega_k0, q0, j0, s0, M). The main loaded assumptions are FLRW/DSR geometry, SIS lens modeling, and the validity of a fourth-order y-expansion at high source redshifts.

free parameters (6)
  • H0 = 67.86 (SGL+PP+DESI), 66.71 (SGL+Union3+DESI), 68.72 (SGL+DESY5+DESI) km/s/Mpc
    Global Hubble constant fitted with flat prior [0,100], constrained mainly by DESI-DR2; nuisance in SN distance moduli.
  • Omega_k0 = 0.139, 0.132, -0.054 with DESI; 0.049, 0.065, -0.031 without DESI
    Spatial curvature parameter fitted through the DSR and cosmographic distances; central to the flatness claim.
  • q0 = -0.481, -0.324, -0.546 with DESI
    Present-day deceleration parameter, a free coefficient in the cosmographic expansion.
  • j0 = 1.163, 0.208, 1.344 with DESI
    Present-day jerk parameter, a free coefficient in the cosmographic expansion.
  • s0 = 2.544, -1.452, 3.335 with DESI
    Present-day snap parameter, a free coefficient in the cosmographic expansion; weakly constrained.
  • M = not reported (marginalized)
    Supernova absolute-magnitude nuisance parameter marginalized in Eq. (2.15).
axioms (5)
  • domain assumption FLRW metric and distance sum rule (Eq. 2.9) are valid
    The DSR identity is exact for FLRW geometry; the paper's model-independence claim inherits this assumption.
  • ad hoc to paper Fourth-order y-redshift cosmographic expansion is accurate for z_s up to ~3.6
    No convergence or truncation test is given; source redshifts reach y ~ 0.78, where higher-order terms can matter.
  • domain assumption SIS mass profile for all 161 lenses with a 3% systematic uncertainty
    Converts velocity dispersions to distance ratios via Eq. (2.1); mass-profile deviations would bias Omega_k0 and cosmographic parameters.
  • domain assumption Aperture correction eta = -0.066 +/- 0.035 and formulas (2.2)-(2.3)
    Adopted from prior spectroscopy; the uncertainty is propagated, but the formula itself is an input.
  • ad hoc to paper Formulas for distance expansions and SN marginalization from Paper I are correct
    Core derivations are not reproduced here; the paper depends on its companion for details.

pith-pipeline@v1.3.0-alltime-deepseek · 14992 in / 16976 out tokens · 169090 ms · 2026-08-04T00:27:22.653646+00:00 · methodology

0 comments
read the original abstract

The distance ratios derived from strong lensing systems, combined with complementary cosmological observations, allow for the study of cosmic expansion and curvature without assuming a fixed background cosmological model. In this work, we perform an analysis of cosmic expansion using the latest Type Ia supernova samples, including PantheonPlus, Union3, and DES Y5, combined with baryon acoustic oscillation dataset from DESI DR2 and strong-lensing distance ratios. The cosmic expansion is carried out to fourth order in the variable $y = z/(1+z)$, which allows constraints on the present-day deceleration, jerk, and snap parameters $(q_0, j_0, s_0)$. The analysis utilizes the distance sum rule to provide an independent determination of the spatial curvature parameter $\Omega_{k0}$ without assuming any specific cosmological dynamics. Our results from combining strong lensing distance ratios with each supernova dataset indicate that a flat Universe remains consistent at the 95\% confidence level, and the inclusion of DESI-DR2 measurements tightens the parameter intervals while preserving agreement with flat geometry at the 68\% confidence level, in line with standard cosmology. The inferred values of $q_0$ and $j_0$ are compatible with $\Lambda$CDM predictions for all dataset combinations. The constraints on $s_0$ remain weak, although modest improvement appears after DESI DR2 data are included. This work represents the second and final paper in the two-part cosmography study.

discussion (0)

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