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arxiv: 2502.02243 · v4 · submitted 2025-02-04 · 🌌 astro-ph.CO

Novel geometrical test of cosmological expansion from photometric data

David Touzeau , Francis Bernardeau , Karim Benabed , Sandrine Codis This is my paper

Pith reviewed 2026-05-23 04:29 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords weak lensingBNT transformcosmological expansiondark energy equation of statetomographic cosmic shearnull testEuclid
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The pith

BNT transform nulls low-redshift lens contributions in weak lensing maps to test cosmological expansion independently of matter clustering.

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

The paper shows that the BNT transform applied to tomographic cosmic-shear data creates weak lensing maps where low-redshift lens effects are removed. This removal depends only on the universe's expansion rate and holds regardless of how matter is distributed, even at small nonlinear scales. The resulting maps enable a null test that isolates background evolution information from large-scale structure data. Fisher matrix calculations indicate this can tighten bounds on the dark energy equation of state, though shape noise currently restricts the gains.

Core claim

The BNT transform allows construction of weak lensing transformed maps for which the contribution from low redshift lenses is nulled. As this transformation depends specifically on the expansion rate of the Universe but is independent of the matter distribution properties, it can be leveraged to extract information from large-scale structure probes at arbitrary non-linear scales, providing constraints on cosmological background evolution. Fisher matrix analysis shows this approach can substantially enhance constraints on the dark energy equation of state for stage IV projects.

What carries the argument

The BNT (Bernardeau, Nishimichi, Taruya) transform, which constructs transformed weak lensing maps that null low-redshift lens contributions by depending only on the expansion history.

If this is right

  • Constraints on cosmological background evolution become available from data at arbitrary nonlinear scales.
  • Constraints on the dark energy equation of state are enhanced for stage IV weak lensing surveys.
  • A specific null test for cosmological expansion is enabled without assumptions about matter distribution.
  • Shape noise currently limits performance, but future survey designs can increase effectiveness.

Where Pith is reading between the lines

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

  • The method could be applied to existing photometric catalogs to obtain early, scale-independent checks on expansion history.
  • Combining BNT-transformed maps with other probes such as baryon acoustic oscillations might isolate expansion signals more cleanly.
  • Survey strategies that lower shape noise would directly increase the statistical power of this null test.

Load-bearing premise

The BNT transformation depends specifically on the expansion rate of the Universe but is independent of the matter distribution properties.

What would settle it

Apply the BNT transform to simulated weak lensing maps with a fixed expansion history but deliberately varied matter clustering properties; if the nulled maps still show residual low-redshift signals or clustering dependence, the independence claim fails.

Figures

Figures reproduced from arXiv: 2502.02243 by David Touzeau, Francis Bernardeau, Karim Benabed, Sandrine Codis.

Figure 1
Figure 1. Figure 1: Shape of the nulled lensing kernels ˆwa(z) (solid lines) constructed for 10 equally populated bins and of original lensing kernels wi(z) (dashed lines). The transformation is built from the two following quan￾tities or "moments" n (0) i = Z dχ ni(χ) and n (1) i = Z dχ ni(χ) FK(χ) , (5) where we define3 FK(χ) =    c H0 tan √ KχH0/c  √ K for K > 0, χ for K = 0, c H0 tanh √ −KχH0/c  √ −K … view at source ↗
Figure 2
Figure 2. Figure 2: Value of the FoM for the parameters w0, wa, obtained with nulling and with or without Planck’s prior on Ωm, as a function of the number density of sources to be used for shear measurements. One can see in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Triangle plot for sampled parameters {Ωm, w0, Q3} with large uniform priors in blue and Planck+BAO w0-CDM constraint as a prior for Ωm in red. Dashed lines show the fiducial values of parameters. plot shows the localisation of the Ωm − w0 degeneracy in the nulling only case. This is actually inherited from the global degeneracy deriving from Eq. (8) (see [2] for details). We can actually see that this dire… view at source ↗
read the original abstract

In tomographic cosmic-shear observations, the BNT (Bernardeau, Nishimichi, Taruya) transform, Bernardeau et al. (2014), allows to build weak lensing transformed maps for which the contribution from low redshift lenses is nulled. As this transformation depends specifically on the expansion rate of the Universe but is independent of the matter distribution properties, it can be leveraged to extract information from large-scale structure probes at arbitrary non-linear scales, providing constraints on cosmological background evolution. We demonstrate this by proposing a specific null test for stage IV weak lensing projects. Using a Fisher matrix analysis and parameter sampling, we show that this approach can substantially enhance constraints on the dark energy equation of state. Notably, we find that shape noise currently limits this method's effectiveness making significant improvement possible in future designs. A detailed analysis of our null test in the context of the Euclid mission is presented in a companion paper Touzeau et al. (2025).

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 / 0 minor

Summary. The paper claims that the BNT transform applied to tomographic cosmic shear data constructs nulled maps in which low-redshift lens contributions vanish. Because the transform weights depend only on the expansion history (comoving distances) and not on matter clustering, the resulting maps furnish a null test that isolates geometric information on background evolution. Fisher-matrix and sampling forecasts are presented showing that this test substantially tightens constraints on the dark-energy equation-of-state parameters w0 and wa for Stage-IV surveys, although shape noise is identified as the current limiting factor.

Significance. If the claimed separation between geometry and growth can be demonstrated, the method would supply a genuinely new, scale-independent probe of expansion history from photometric weak-lensing data. The explicit use of both Fisher and sampling analyses, together with the existence of a companion Euclid-specific study, strengthens the practical relevance of the result.

major comments (2)
  1. [Abstract] Abstract: the central assertion that the BNT transform 'is independent of the matter distribution properties' and therefore yields constraints on background evolution alone is not yet supported by the visible analysis. The nulled shear field remains an integral of the residual kernel against δ_m(k,z) at the surviving (higher) redshifts; any Fisher or sampling result that reports improved w0/wa bounds must therefore either marginalize over growth parameters or demonstrate that the geometric information is extracted without residual degeneracy. No such demonstration is visible in the abstract or the described results.
  2. [Abstract (Fisher and sampling results)] The Fisher-matrix and sampling sections (referenced in the abstract) report an 'enhancement' in dark-energy constraints, yet the parameter space, priors on growth/amplitude parameters, and treatment of the residual high-z power spectrum are not specified. Without these details it is impossible to judge whether the reported improvement arises from the geometric nulling or from implicit assumptions that fix the matter power spectrum.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address each major comment below and will revise the manuscript to improve clarity in the abstract and methods sections.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central assertion that the BNT transform 'is independent of the matter distribution properties' and therefore yields constraints on background evolution alone is not yet supported by the visible analysis. The nulled shear field remains an integral of the residual kernel against δ_m(k,z) at the surviving (higher) redshifts; any Fisher or sampling result that reports improved w0/wa bounds must therefore either marginalize over growth parameters or demonstrate that the geometric information is extracted without residual degeneracy. No such demonstration is visible in the abstract or the described results.

    Authors: The BNT weights are derived solely from the comoving distance-redshift relation and contain no dependence on the matter power spectrum amplitude, shape, or growth function; this is the sense in which the transform is independent of matter-distribution properties. The nulled maps retain higher-redshift contributions, but the nulling condition itself encodes geometric information. In the reported forecasts we marginalize over growth and amplitude parameters, so that any tightening of w0/wa bounds arises from the geometry-dependent nulling. We will revise the abstract to state this marginalization explicitly and to clarify the separation between the transform weights and the residual high-z signal. revision: yes

  2. Referee: [Abstract (Fisher and sampling results)] The Fisher-matrix and sampling sections (referenced in the abstract) report an 'enhancement' in dark-energy constraints, yet the parameter space, priors on growth/amplitude parameters, and treatment of the residual high-z power spectrum are not specified. Without these details it is impossible to judge whether the reported improvement arises from the geometric nulling or from implicit assumptions that fix the matter power spectrum.

    Authors: We agree that the abstract and main text should specify these elements. The parameter space comprises the standard cosmological parameters together with w0 and wa; growth and amplitude parameters are marginalized with flat priors. The residual high-z power spectrum is evaluated at the surviving redshifts using the usual linear-to-non-linear mapping without fixing its amplitude. We will expand the abstract and add a short methods subsection that lists the full parameter set, priors, and high-z treatment, thereby demonstrating that the reported improvement is attributable to the geometric information. revision: yes

Circularity Check

0 steps flagged

No circularity: BNT properties from 2014 derivation; Fisher forecasts use standard methods

full rationale

The paper applies the BNT transform whose geometric nulling property (dependence on expansion history via comoving distances, independence from matter clustering) is taken directly from the 2014 Bernardeau et al. reference. This prior derivation is external to the present work even though one author overlaps. The current manuscript then defines a null test and runs ordinary Fisher-matrix and MCMC forecasts on stage-IV survey specifications; neither step re-derives the BNT weights nor fits any parameter that is later renamed as a prediction. No equation reduces to its own input by construction, no uniqueness theorem is invoked from self-citation, and the central claim remains a straightforward application of an independently published mathematical construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the geometric properties of the BNT transform as introduced in prior work; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The BNT transform nulls low-redshift lens contributions based solely on the expansion rate and is independent of matter distribution properties.
    This is the key property stated in the abstract that enables the null test.

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Reference graph

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