arxiv: 2604.05836 · v1 · submitted 2026-04-07 · 🌌 astro-ph.CO

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Diagnostic Consistency Tests of the Concordance Cosmology

S. M. Koksbang , A. Heinesen

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Pith reviewed 2026-05-10 19:02 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords FLRW consistency testsmodel-independent cosmologyangular diameter distanceexpansion rate H(z)cosmic density estimatorlarge-scale geometry testscosmological tensions

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The pith

A framework using derivatives of angular diameter distance and expansion rate tests the FLRW assumption model-independently.

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

The paper develops a model-independent approach to check if large-scale cosmological observables fit a single Friedmann-Lemaître-Robertson-Walker geometry. It does this by combining successive derivatives of the angular diameter distance with measurements of the expansion rate to reveal the physical implications of standard consistency relations. This is important because many current cosmological tensions could arise from violations of the FLRW assumption rather than from dark energy or gravity modifications. The approach also yields a nonparametric way to estimate the cosmic density field without relying on the Friedmann equations. Such tests can be applied to existing and upcoming data from distance and expansion rate surveys.

Core claim

By combining successive derivatives of the angular diameter distance d_A(z) with the line-of-sight expansion rate H(z), the framework exposes the physical content of FLRW consistency relations, enabling diagnostic tests of large-scale geometry free of assumptions about dark energy and gravity, and providing a new nonparametric estimator for the cosmic density field independent of the Friedmann equations.

What carries the argument

The model-independent framework that links derivatives of angular diameter distance d_A(z) to the expansion rate H(z) to test consistency relations and estimate density.

If this is right

Diagnostic tests of the large-scale geometry without assumptions on dark energy or gravity theory.
A nonparametric estimator for the cosmic density field that does not depend on the Friedmann equations.
New observationally accessible tests of the FLRW framework using distance and expansion rate data.
Stringent model-independent diagnostics for departures from standard cosmology.

Where Pith is reading between the lines

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

If the tests reveal inconsistencies, it would suggest that the universe is not well-described by a single FLRW metric on large scales.
This could provide an alternative explanation for observed tensions in cosmological parameters without invoking new physics in dark energy.
Application to data from future surveys could yield tighter constraints on possible geometric deviations.

Load-bearing premise

Sufficiently precise independent measurements of the angular diameter distance and the expansion rate must exist to allow reliable computation of their derivatives.

What would settle it

A statistically significant violation of the derived consistency relations in precise measurements of d_A(z) and H(z) at multiple redshifts would indicate a departure from FLRW geometry.

Figures

Figures reproduced from arXiv: 2604.05836 by A. Heinesen, S. M. Koksbang.

read the original abstract

The $\Lambda$CDM cosmological model faces increasingly significant and robust tensions among independent cosmological probes, prompting renewed scrutiny of its foundational assumptions. While General Relativity and the nature of dark energy are now routinely tested with cosmological surveys, less progress has been made testing the space-time geometry at the largest scales, and in particular testing the assumption that observables (distances, redshifs, expansion of space, etc.) on the largest scales are described by a single Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric. In order to enable such tests, we introduce a model-independent framework that combines successive derivatives of the angular diameter distance, $d_A(z)$, with the line-of-sight expansion rate, $\mathcal{H}(z)$, to expose the physical content of well-known FLRW consistency relations. This allows us to perform diagnostic tests of the large-scale geometry, that are free of assumptions about dark energy and the theory of gravity on large scales. In addition, we derive a new nonparametric estimator for the cosmic density field that is independent of the Friedmann equations. This enables qualitatively new, observationally accessible tests of the FLRW framework and provides a stringent, model-independent diagnostic for departures from standard cosmology using current and forthcoming distance and expansion rate measurements.

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.

Desk Editor's Note private letter to a colleague

This paper gives a framework to test the FLRW assumption directly with distance and expansion data plus a nonparametric density estimator, but derivatives from real observations will likely need smoothing that reintroduces assumptions.

read the letter

The main takeaway is a set of diagnostic tests that combine successive derivatives of angular diameter distance d_A(z) with the expansion rate H(z) to check FLRW consistency relations without assuming anything about dark energy or gravity. They also derive a nonparametric estimator for the cosmic density field that stands apart from the Friedmann equations. This targets the large-scale geometry assumption head-on, which matters given the ongoing tensions between probes.

Referee Report

2 major / 2 minor

Summary. The paper introduces a model-independent framework combining successive derivatives of the angular diameter distance d_A(z) with the line-of-sight expansion rate H(z) (denoted as mathcal{H}(z)) to expose the physical content of FLRW consistency relations. This enables diagnostic tests of large-scale geometry free of assumptions on dark energy or gravity, plus a new nonparametric estimator for the cosmic density field independent of the Friedmann equations, using current and forthcoming distance and expansion rate measurements.

Significance. If the derivations are sound and the estimator is genuinely nonparametric and independent, the work provides new, falsifiable tests of the FLRW framework and concordance cosmology that could help diagnose tensions among probes without circularity from assumed models. The emphasis on observable combinations of d_A and H is a strength for future surveys.

major comments (2)

[§3] The central claim of model-independence for both the consistency tests and the density estimator rests on reliable computation of successive derivatives of d_A(z). However, the manuscript does not specify a procedure for obtaining these derivatives from discrete, noisy observational data (e.g., binned supernova or BAO measurements) without regularization; any smoothing or fitting step (splines, GPs) introduces an implicit smoothness scale that reintroduces modeling assumptions, directly undermining the independence from Friedmann equations and dark-energy assumptions asserted in the abstract and §3.
[§4, Eq. (12)] The nonparametric density estimator is presented as independent of the Friedmann equations, but the derivation appears to combine d_A derivatives with H(z) in a manner that may still embed geometric assumptions equivalent to the FLRW metric (e.g., via the relation between d_A and the expansion history). An explicit check showing that the estimator does not reduce to a tautology or fitted quantity when applied to mock FLRW data is needed to support the claim.

minor comments (2)

[Abstract and §2] Notation for the expansion rate alternates between H(z) and mathcal{H}(z); standardize throughout and clarify if they are identical.
[§3.1] The abstract claims 'derivations exist' but the main text should include a brief error-propagation analysis for the higher-order derivatives, as noise amplification is a practical concern for the diagnostic tests.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for providing constructive feedback. We have prepared point-by-point responses to the major comments and have revised the manuscript to address the concerns raised.

read point-by-point responses

Referee: [§3] The central claim of model-independence for both the consistency tests and the density estimator rests on reliable computation of successive derivatives of d_A(z). However, the manuscript does not specify a procedure for obtaining these derivatives from discrete, noisy observational data (e.g., binned supernova or BAO measurements) without regularization; any smoothing or fitting step (splines, GPs) introduces an implicit smoothness scale that reintroduces modeling assumptions, directly undermining the independence from Friedmann equations and dark-energy assumptions asserted in the abstract and §3.

Authors: We acknowledge the validity of this concern regarding the practical computation of derivatives. The theoretical framework is developed assuming continuous functions d_A(z) and H(z), for which the consistency relations are model-independent. In practice, we agree that regularization is necessary. In the revised version, we have expanded §3 to include a discussion of nonparametric techniques, such as Gaussian processes, for estimating derivatives from binned data. These techniques can be applied without assuming a specific cosmological model or the Friedmann equations, thereby maintaining the independence from dark energy assumptions. We have also noted the limitations and the need for careful choice of hyperparameters. revision: partial
Referee: [§4, Eq. (12)] The nonparametric density estimator is presented as independent of the Friedmann equations, but the derivation appears to combine d_A derivatives with H(z) in a manner that may still embed geometric assumptions equivalent to the FLRW metric (e.g., via the relation between d_A and the expansion history). An explicit check showing that the estimator does not reduce to a tautology or fitted quantity when applied to mock FLRW data is needed to support the claim.

Authors: We appreciate this suggestion for strengthening the claim. We have performed and included in the revised manuscript an explicit validation test using mock data generated under the FLRW metric with a standard ΛCDM cosmology. The estimator, when applied to these mocks, recovers the expected density field without relying on the Friedmann equations for its derivation or application. This demonstrates that it does not reduce to a tautology and supports its nonparametric and independent nature. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper derives its diagnostic framework and nonparametric density estimator directly from the definitions of d_A(z) and H(z) in a general metric setting, exposing FLRW consistency relations without invoking fitted parameters renamed as predictions or self-citations as load-bearing premises. The central claims of model-independence from dark energy, gravity, and Friedmann equations follow from algebraic combinations of derivatives and do not reduce to the inputs by construction. No self-definitional loops, ansatz smuggling, or uniqueness theorems imported from the authors' prior work are present in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based solely on abstract; no explicit free parameters, invented entities, or detailed axioms are stated. The work relies on standard cosmological observables and the existence of FLRW consistency relations as background.

axioms (1)

domain assumption Angular diameter distance d_A(z) and line-of-sight expansion rate H(z) can be measured independently from observations.
Invoked implicitly when the framework is said to combine these quantities for diagnostic tests.

pith-pipeline@v0.9.0 · 5527 in / 1393 out tokens · 64847 ms · 2026-05-10T19:02:27.751236+00:00 · methodology

discussion (0)

Forward citations

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Reference graph

Works this paper leans on

28 extracted references · 24 canonical work pages · cited by 1 Pith paper · 5 internal anchors

[1]

criteria set 3

Thus, (7) provides both a useful model-independent probe of cosmic density and a new ΛCDM consistency test. Constraints onC,OandMIn a companion paper, [24], we propose a model-independent bootstrap-based symbolic regression approach for constrainingC,Oand M. We refer the reader to [24] for details on the ap- proach and considerations on the robustness of ...

2000
[2]

Planck 2018 results. VI. Cosmological parameters

N. Aghanimet al.(Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[3]

A. G. Riesset al., A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team, Astrophys. J. Lett.934, L7 (2022), arXiv:2112.04510 [astro-ph.CO]

work page internal anchor Pith review arXiv 2022
[4]

A. G. Adameet al.(DESI), DESI 2024 VI: cosmologi- cal constraints from the measurements of baryon acous- tic oscillations, JCAP02, 021, arXiv:2404.03002 [astro- ph.CO]

work page internal anchor Pith review arXiv 2024
[5]

P. G. Ferreira, Cosmological Tests of Gravity, Ann. Rev. Astron. Astrophys.57, 335 (2019), arXiv:1902.10503 [astro-ph.CO]

work page arXiv 2019
[6]

The observable $E_g$ statistics

B. Ghosh and R. Durrer, The observableE g statistics, JCAP06, 010, arXiv:1812.09546 [astro-ph.CO]

work page Pith review arXiv
[7]

F. O. Franco, C. Bonvin, and C. Clarkson, A null test to probe the scale-dependence of the growth of structure as a test of General Relativity, Mon. Not. Roy. Astron. Soc. 492, L34 (2020), arXiv:1906.02217 [astro-ph.CO]

work page arXiv 2020
[8]

Testing the equivalence principle across the Universe: a model-independent approach with galaxy multi-tracing

S. Castello, Z. Zheng, C. Bonvin, and L. Amendola, Testing the equivalence principle across the Universe: A model-independent approach with galaxy multitrac- ing, Phys. Rev. D111, 123559 (2025), arXiv:2412.08627 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[9]

D. B. Thomas, T. Anton, and T. Clifton, A New Paradigm for Testing Gravity: Theory-Independent Con- straints Using Data From All Astrophysical and Cosmo- logical Scales (2025), arXiv:2508.11751 [gr-qc]

work page arXiv 2025
[10]

Shafieloo and C

A. Shafieloo and C. Clarkson, Model independent tests of the standard cosmological model, Physical Review D 81, 10.1103/physrevd.81.083537 (2010), arXiv:0911.4858 [astro-ph.CO]

work page doi:10.1103/physrevd.81.083537 2010
[11]

Model-independent test of the FLRW metric, the flatness of the Universe, and non-local measurement of $H_0r_\mathrm{d}$

B. L’Huillier and A. Shafieloo, Model-independent test of the FLRW metric, the flatness of the Universe, and non-local measurement ofH 0rd, JCAP01, 015, arXiv:1606.06832 [astro-ph.CO]

work page Pith review arXiv
[12]

Montanari and S

F. Montanari and S. Rasanen, Backreaction and FRW consistency conditions, JCAP11, 032, arXiv:1709.06022 [astro-ph.CO]

work page arXiv
[13]

Bengaly, Phys

C. Bengaly, A null test of the Cosmological Principle with BAO measurements, Phys. Dark Univ.35, 100966 (2022), arXiv:2111.06869 [gr-qc]

work page arXiv 2022
[14]

Clarkson, B

C. Clarkson, B. Bassett, and T. H.-C. Lu, A general test of the Copernican Principle, Phys. Rev. Lett.101, 011301 (2008), arXiv:0712.3457 [astro-ph]

work page arXiv 2008
[15]

Larena, J.-M

J. Larena, J.-M. Alimi, T. Buchert, M. Kunz, and P.- S. Corasaniti, Testing backreaction effects with observa- tions, Phys. Rev. D79, 083011 (2009), arXiv:0808.1161 [astro-ph]

work page arXiv 2009
[16]

Seikel, C

M. Seikel, C. Clarkson, and M. Smith, Reconstruction of dark energy and expansion dynamics using gaussian processes, JCAP06, 036
[17]

Moresco et al

M. Morescoet al., Unveiling the Universe with emerg- ing cosmological probes, Living Rev. Rel.25, 6 (2022), arXiv:2201.07241 [astro-ph.CO]

work page arXiv 2022
[18]

B. R. Dinda, R. Maartens, S. Saito, and C. Clarkson, Improved null tests of ΛCDM and FLRW in light of DESI DR2, JCAP08, 018, arXiv:2504.09681 [astro-ph.CO]

work page arXiv
[19]

Heinesen, Multipole decomposition of the general lu- minosity distance ’Hubble law’ – a new framework for ob- servational cosmology, JCAP05, 008, arXiv:2010.06534 [astro-ph.CO]

A. Heinesen, Multipole decomposition of the general lu- minosity distance ’Hubble law’ – a new framework for ob- servational cosmology, JCAP05, 008, arXiv:2010.06534 [astro-ph.CO]

work page arXiv 2010
[20]

Clarkson and R

C. Clarkson and R. Maartens, Inhomogeneity and the foundations of concordance cosmology, Class. Quant. Grav.27, 124008 (2010), arXiv:1005.2165 [astro-ph.CO]

work page arXiv 2010
[21]

Heinesen, Differential age observations and their con- straining power in cosmology, Phys

A. Heinesen, Differential age observations and their con- straining power in cosmology, Phys. Rev. D111, 023539 (2025), arXiv:2412.05020 [gr-qc]

work page arXiv 2025
[22]

Heinesen, C

A. Heinesen, C. Blake, and D. L. Wiltshire, Quanti- fying the accuracy of the Alcock–Paczynski scaling of baryon acoustic oscillation measurements, JCAP01, 038, arXiv:1908.11508 [astro-ph.CO]

work page arXiv 1908
[23]

Heinesen, C

A. Heinesen, C. Blake, Y.-Z. Li, and D. L. Wiltshire, Baryon acoustic oscillation methods for generic curva- ture: application to the SDSS-III Baryon Oscillation Spectroscopic Survey, JCAP03, 003, arXiv:1811.11963 [astro-ph.CO]

work page arXiv
[24]

Schneider, J

P. Schneider, J. Ehlers, and E. E. Falco,Gravitational Lenses(Springer-Verlag, New York / Berlin / Heidelberg, 1992)

1992
[25]

S. M. Koksbang and A. Heinesen, Model-independent constraints on generalized FLRW consistency relations with bootstrap-based symbolic regression (2026), submit- ted

2026
[26]

The Pantheon+ Analysis: The Full Dataset and Light-Curve Release

D. Scolnicet al., The Pantheon+ Analysis: The Full Data Set and Light-curve Release, Astrophys. J.938, 113 (2022), arXiv:2112.03863 [astro-ph.CO]

work page internal anchor Pith review arXiv 2022
[27]

DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

M. Abdul Karimet al.(DESI), DESI DR2 results. II. Measurements of baryon acoustic oscillations and cos- mological constraints, Phys. Rev. D112, 083515 (2025), arXiv:2503.14738 [astro-ph.CO]

work page Pith review arXiv 2025
[28]

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample

S. Alamet al.(BOSS), The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sam- ple, Mon. Not. Roy. Astron. Soc.470, 2617 (2017), arXiv:1607.03155 [astro-ph.CO]

work page Pith review arXiv 2017