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arxiv: 2512.15604 · v2 · pith:EQREVKWBnew · submitted 2025-12-17 · 🌌 astro-ph.CO

Comparing cosmic shear nulling methods for Stage-IV surveys

Naomi Clare Robertson , Alex Hall This is my paper

Pith reviewed 2026-05-16 21:20 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords cosmic shearnulling methodsbaryon feedbackS8dark energyFisher forecastStage-IV surveysBNT transform
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The pith

Nulling strategies can substantially reduce bias on S8 and dark energy parameters in cosmic shear measurements.

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

The paper evaluates three different nulling approaches designed to minimize the effects of baryon feedback on cosmic shear data for future surveys. These methods transform the data vector to suppress contributions from high-k modes where baryons introduce uncertainties. Using Fisher forecasts, the authors demonstrate that these nulling techniques can significantly decrease biases in the inferred values of S8 and dark energy parameters. Different methods offer varying balances between bias mitigation and statistical precision, with the cross-correlation approach requiring additional galaxy clustering data. This is relevant because uncontrolled baryon effects could otherwise limit the cosmological insights from precision lensing surveys.

Core claim

Applying nulling transformations to cosmic shear data vectors, including the BNT transform on the lensing field, LU factorization of the Limber integral, and cross-correlation with large-scale structure tracers, effectively reduces the bias from baryon feedback on cosmological constraints such as S8 and dark energy equation of state parameters, as shown in Fisher matrix forecasts for Stage-IV surveys.

What carries the argument

Nulling transformations applied to the cosmic shear data vector to suppress high-k modes influenced by baryonic physics.

Load-bearing premise

The Fisher forecast model accurately represents the bias reduction from nulling without needing full end-to-end simulations or real data validation, and the assumed baryon feedback model matches reality.

What would settle it

Comparing the bias reductions predicted by the Fisher forecasts to those obtained from applying the nulling methods to simulated mock datasets or real observational data from Stage-III surveys.

Figures

Figures reproduced from arXiv: 2512.15604 by Alex Hall, Naomi Clare Robertson.

Figure 1
Figure 1. Figure 1: Redshift distributions for six tomographic bins, which are used to produce mock power spectra. For the case of the cross-correlation method we take the two lowest redshift bins as our lens sample and the three highest red￾shift bins as our source sample, ignoring the third redshift bins to minimise overlap between the lens and source sam￾ple. z 0.0 0.2 0.4 0.6 0.8 1.0 q i(z) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 z 0… view at source ↗
Figure 2
Figure 2. Figure 2: The top panel shows the lensing kernels, q i (z) for the six tomographic bins shown in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Impact of baryon feedback, assuming ΘAGN = 7.8, on the cosmic shear power spectra for the ‘standard’ case (or￾ange), the BNT transformed case (blue) and the cross-correlation case (red). In all but the (0,0) bin pair, the BNT transformed spectra is less impacted by baryons, particularly considering higher redshift bin pairs. The cross-correlation-modified spectra are least impacted by baryons for the highe… view at source ↗
Figure 5
Figure 5. Figure 5: Power spectra for each pair of tomographic bins including contribution from different ranges in k: the dashed line corresponds to the smallest scales with contributions from k > 0.5h/Mpc, the solid line corresponds to slightly larger scales (0.1 < k < 0.5)h/Mpc and the dotted line shows the full spectra including all k. The ‘standard’ case (orange) shows small scales contribute to even the smallest ℓ-modes… view at source ↗
Figure 6
Figure 6. Figure 6: Performance of the LUnul method for ℓ=500. Upper left panel: the Limber integrand for each bin pair in our fiducial setup. Different colours refer to different bin pairs, with darker colours corresponding to closer source bins. Lower left panel: cumulative contribution across k, normalized to unity. Upper right panel: Limber integrand after applying the LUnul transform. Colours now refer to elements of the… view at source ↗
Figure 7
Figure 7. Figure 7: A cut in ℓ for each tomographic bin defined for a given value of k using Equation 13. For the BNT case we use the BNT transformed lensing kernels shown in the lower panel of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Constraints on parameters {S8,Ωm,w0,wa} for a range of scale cuts, defined in k and transformed to ℓ for each tomographic bin, for the four different methods considered in this analysis: the left column shows each parameter constraint with corresponding 1σ error bars and the fiducial parameter value shown by the horizontal line, the centre column shows the error, and the right column shown the parameter bi… view at source ↗
Figure 9
Figure 9. Figure 9: The one and two-dimensional constraints on parameters for all three nulling methods considered, compared to the standard cosmic shear, and for four example sets of scale cuts. REFERENCES Abbott T. M. C., et al., 2022, Phys. Rev. D, 105, 023520 Akino D., et al., 2022, PASJ, 74, 175 Amara A., Réfrégier A., 2008, MNRAS, 391, 228 Amodeo S., et al., 2021, Phys. Rev. D, 103, 063514 Amon A., et al., 2022, Phys. R… view at source ↗
Figure 10
Figure 10. Figure 10: The figure-of-bias and figure-of-merit for the (w0,wa) constraint. In the upper panel the grey regions correspond to the 1 and 2σ level of bias in the 2D parameter space. McCarthy I. G., et al., 2024, arXiv e-prints, p. arXiv:2410.19905 Mead A. J., Brieden S., Tröster T., Heymans C., 2021, MNRAS, 502, 1401 Moreira M. G., Andrade-Oliveira F., Fang X., Huang H.-J., Krause E., Miranda V., Rosenfeld R., Simon… view at source ↗
Figure 11
Figure 11. Figure 11: This figure is the power spectrum version of [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
read the original abstract

We present an analysis comparing nulling strategies for reducing the impact of baryon feedback on cosmic shear measurements. We consider three different approaches which aim to `null' the high-$k$ modes using transformations applied to the data vector: the Bernardeau-Nishimichi-Taruya (BNT) transform which operates on the lensing field, a new implementation of an LU factorisation of the discretized Limber integral (LUnul) which operates on the lensing two-point statistics, and finally a method which uses a correlated LSS tracers to suppress contributions from lower redshifts (cross-correlation). We compare these methods to un-nulled (or standard) cosmic shear at the data vector level and assess whether these methods are able to reduce the bias on cosmological constraints using a Fisher forecast. We find that the nulling techniques considered can have a large impact on reducing the bias on $S_8$ and Dark Energy parameters. The cross-correlation method is effective at reducing biases in $S_8$, but requires additional information from galaxy clustering. The LUnul method is the most aggressive of the methods and hence reduces biases most efficiently as $k_{\rm max}$ is increased, although this improvement in accuracy comes at the cost of precision. The BNT approach preserves more information than LUnul, and has a more rigorous theoretical grounding. We demonstrate that all three of these methods are effective at mitigating bias, and can be readily applied in forthcoming lensing analyses.

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 compares three nulling techniques—BNT transform on the lensing field, LUnul (LU factorization of the discretized Limber integral) on the two-point statistics, and cross-correlation with LSS tracers—to suppress high-k baryon feedback contributions in cosmic shear data vectors. Using Fisher-matrix forecasts, it evaluates bias reduction on S8 and dark-energy parameters (w0/wa) relative to standard cosmic shear, concluding that all three methods mitigate bias effectively, with LUnul being most aggressive (at precision cost), BNT preserving more information with stronger theoretical grounding, and cross-correlation requiring extra galaxy-clustering data.

Significance. If the reported bias reductions hold, the work supplies a timely, quantitative comparison that can guide analysis choices for Stage-IV surveys (LSST, Euclid, Roman). It explicitly quantifies trade-offs between bias mitigation and information loss, and the BNT method's rigorous grounding is a clear strength. The significance is reduced, however, by the exclusive reliance on Fisher forecasts without mock validation or sensitivity tests to modeling choices.

major comments (2)
  1. [Fisher forecast setup and results] Fisher-forecast section (methods and results): the central claim that the three nulling transforms produce 'large impact on reducing the bias on S8 and Dark Energy parameters' rests on the assumption that the Fisher matrix accurately captures the post-nulling bias reduction. This assumption is load-bearing because the forecast uses a single baryon-feedback model, Gaussian likelihood, and linear response; it does not propagate the covariance reshaping or non-Gaussianity induced by aggressive nulling (especially LUnul). A concrete mock-based validation would be required to confirm the quoted bias reductions translate to real analyses.
  2. [Results comparison] Results comparison (likely §4–5): the statement that LUnul 'reduces biases most efficiently as k_max is increased' is not accompanied by a quantitative figure-of-merit loss or explicit error-bar inflation relative to BNT; without these numbers the claimed precision–accuracy trade-off remains qualitative and cannot be directly used by Stage-IV analysts.
minor comments (2)
  1. [Abstract and method description] Abstract and §2: the description of the 'new implementation of an LU factorisation' lacks a brief equation or reference to the exact discretization of the Limber integral; adding one line would clarify how LUnul differs from prior work.
  2. [Throughout] Notation: the transformed data vectors for the three methods are denoted inconsistently across sections; standardizing the symbol (e.g., d_nulled) would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major comment below and have made revisions to strengthen the presentation of our Fisher-forecast results.

read point-by-point responses

  1. Referee: Fisher-forecast section (methods and results): the central claim that the three nulling transforms produce 'large impact on reducing the bias on S8 and Dark Energy parameters' rests on the assumption that the Fisher matrix accurately captures the post-nulling bias reduction. This assumption is load-bearing because the forecast uses a single baryon-feedback model, Gaussian likelihood, and linear response; it does not propagate the covariance reshaping or non-Gaussianity induced by aggressive nulling (especially LUnul). A concrete mock-based validation would be required to confirm the quoted bias reductions translate to real analyses.

    Authors: We agree that Fisher forecasts rely on simplifying assumptions and do not capture non-Gaussian covariance effects or the full impact of nulling on the data-vector covariance. These methods are nevertheless the standard approach for controlled, apples-to-apples comparisons of analysis techniques in Stage-IV forecasts. In the revised manuscript we have added an explicit discussion of these limitations (new paragraph in Section 6), including the choice of a single baryon-feedback model and the Gaussian likelihood assumption, and we note that end-to-end mock validation would be a valuable extension for future work. The relative ordering of the three nulling methods remains robust under the consistent set of assumptions used here. revision: partial

  2. Referee: Results comparison (likely §4–5): the statement that LUnul 'reduces biases most efficiently as k_max is increased' is not accompanied by a quantitative figure-of-merit loss or explicit error-bar inflation relative to BNT; without these numbers the claimed precision–accuracy trade-off remains qualitative and cannot be directly used by Stage-IV analysts.

    Authors: We thank the referee for this suggestion. In the revised manuscript we now provide quantitative metrics for the precision–accuracy trade-off. Specifically, we report the DETF dark-energy figure of merit and the fractional increase in the 1σ marginalized errors on S8, w0 and wa for LUnul relative to both BNT and standard cosmic shear, evaluated at several k_max values. These results appear in a new table (Table 3) and are discussed in the updated Section 5, allowing direct use by Stage-IV analysts. revision: yes

Circularity Check

0 steps flagged

No circularity: independent nulling transforms evaluated via standard Fisher forecasts

full rationale

The paper applies three established nulling transformations (BNT on the lensing field, LUnul via LU factorization of the Limber integral, and cross-correlation with LSS tracers) directly to the data vector. Bias reduction on S8 and dark energy parameters is then quantified using standard Fisher matrix forecasts under a fixed baryon feedback model. No step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation; the forecasts are external statistical evaluations independent of the nulling choices themselves. The derivation chain remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields limited visibility into modeling details; standard assumptions in lensing projections and forecasts are inferred.

axioms (2)
  • domain assumption Limber approximation holds for the lensing projections used in the two-point statistics
    Invoked for the discretized Limber integral in LUnul and standard cosmic shear.
  • domain assumption Fisher matrix provides a reliable estimate of parameter biases and covariances
    Central to the assessment of bias reduction on S8 and dark energy parameters.

pith-pipeline@v0.9.0 · 5560 in / 1264 out tokens · 27995 ms · 2026-05-16T21:20:01.975605+00:00 · methodology

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Works this paper leans on

1 extracted references · 1 canonical work pages

  1. [1]

    Abbott T. M. C., et al., 2022, Phys. Rev. D, 105, 023520 Akino D., et al., 2022, PASJ, 74, 175 Amara A., Réfrégier A., 2008, MNRAS, 391, 228 Amodeo S., et al., 2021, Phys. Rev. D, 103, 063514 Amon A., et al., 2022, Phys. Rev. D, 105, 023514 Barthelemy A., Codis S., Uhlemann C., Bernardeau F., Gavazzi R., 2020, MNRAS, 492, 3420 Bernardeau F., Nishimichi T....

    work page arXiv 2022