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It's not $\sigma_8$ : constraining the non-linear matter power spectrum with the Dark Energy Survey Year-5 supernova sample

T0 review · 2 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Using 1,484 supernovae from the Dark Energy Survey Year-5 sample, this paper measures A_mod = 0.77 (+0.69/-0.40), a rescaling of non-linear matter power, finding it consistent with a cold-dark-matter-only universe but hinting at…

desk verdict The canonical A_mod quoted in the abstract is likely a halo-convergence amplitude, not the power-spectrum multiplier claimed; the method is still worth a serious referee. read the letter →

arxiv 2501.19117 v1 pith:BRVPJ4RJ submitted 2025-01-31 astro-ph.CO

Paul Shah , T. M. Davis , M. Vincenzi , P. Armstrong , D. Brout , R. Camilleri , L. Galbany , M. S. S. Gill
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D. Huterer N. Jeffrey O. Lahav J. Lee C. Lidman A. Möller M. Sullivan L. Whiteway P. Wiseman S. Allam M. Aguena J. Annis J. Blazek D. Brooks A. Carnero Rosell J. Carretero C. Conselice L. N. da Costa M. E. S. Pereira S. Desai H. T. Diehl P. Doel S. Everett I. Ferrero B. Flaugher J. Frieman J. García-Bellido E. Gaztanaga G. Giannini D. Gruen R. A. Gruendl G. Gutierrez S. R. Hinton D. L. Hollowood K. Honscheid D. J. James S. Lee J. L. Marshall J. Mena-Fernández R. Miquel A. Palmese A. Pieres A. A. Plazas Malagón A. Porredon S. Samuroff E. Sanchez I. Sevilla-Noarbe M. Smith E. Suchyta M. E. C. Swanson G. Tarle D. L. Tucker N. Weaverdyck
This is my paper · ORCID
classification astro-ph.CO
keywords gravitationallensing:weaktransients:supernovaecosmology:darkmattergalaxies:haloescosmologicalparametersnon-linearpowerspectrum
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the scatter in Type Ia supernova brightness caused by gravitational lensing is set by matter clustering on non-linear scales, so trying to read it as a measurement of $\sigma_8$ (the linear-theory amplitude) is misguided. Instead, the authors introduce an empirical parameter $A_{\rm mod}$ that multiplies the halo contribution to the matter power spectrum, and forward-model the entire non-Gaussian distribution of SN magnifications. Using 1,484 supernovae from the Dark Energy Survey Year-5 sample, they find $A_{\rm mod} = 0.77^{+0.69}_{-0.40}$, consistent with the cold-dark-matter-only expectation of unity but with a posterior that peaks toward suppression and excludes $A_{\rm mod} > 1.09$ at 68% credibility. If the interpretation is right, this is the first SN-based handle on non-linear matter power that is cleanly separated from linear parameters such as $\sigma_8$, opening a new way to test baryon feedback, neutrino mass, and non-standard dark matter.

What carries the argument

The central object is the empirical power-spectrum model $$P(k,z) = P_L(k,z) + A_{\rm mod}\, P_H(k,z),$$ where $P_L$ is the cold-dark-matter linear power spectrum and $P_H$ is the halo contribution, calibrated with the Sheth et al. (2001) mass function refitted by Courtin et al. (2011) and NFW density profiles (Navarro et al. 1997). The lensing magnification probability density is the convolution $p_{\rm lens} = p_L * p_H$, with $p_L$ a zero-mean log-normal linear term and $p_H$ computed from TurboGL's semi-analytic halo integration; $A_{\rm mod}$ acts as a scale parameter on the halo pdf, so $\sigma_H(A_{\rm mod}) = A_{\rm mod}\,\sigma_H(1)$. The SN likelihood is then formed by convolving this lensing pdf with the intrinsic (sin-arcsin) residual distribution and adjusting each diagonal term of the covariance-based Gaussian likelihood (Eqs. 13--15).

What would settle it

Split the DES-SN5YR sample by redshift and fit $A_{\rm mod}$ separately in each bin: if the single-parameter rescaling ansatz is correct, all bins should return the same $A_{\rm mod}$ within uncertainties, whereas scale- or redshift-dependent physics (e.g., baryon feedback that changes shape) would produce significant variation. A more direct test is to ray-trace high-resolution N-body simulations with particle masses near $10^7\,M_\odot$ and softening lengths near 1 kpc to the same redshifts and compare the full magnification pdf against the paper's model; any shape difference that cannot be mimicked by rescaling would invalidate $A_{\rm mod}$ as a faithful probe of non-linear power.

Watch

Extended reading notes

Core claim

Type Ia supernova magnifications are sensitive to the matter power spectrum on scales $k > 1\,h\,{\rm Mpc}^{-1}$, beyond the linear regime, so the dispersion of SN brightness residuals should not be interpreted through $\sigma_8$. The authors forward-model the full probability density function of SN Ia magnification as a function of standard cosmological parameters plus an empirical parameter $A_{\rm mod}$ that rescales only the non-linear halo term. Applied to 1,484 SNe Ia from the DES Year-5 sample, the analysis gives $A_{\rm mod,S} = 0.77^{+0.69}_{-0.40}$ (68% credible interval around the median), consistent with the CDM-only benchmark $A_{\rm mod}=1$; the posterior peaks near $0.30$ and the 68% highest-density interval gives $A_{\rm mod} < 1.09$, so the data hint at power suppression rather than enhancement. The posterior shows little correlation between $A_{\rm mod}$ and $S_8$, demonstrating that SN lensing can separate linear from non-linear power.

Load-bearing premise

The load-bearing premise is that every unknown small-scale effect can be absorbed into a single number $A_{\rm mod}$ that simply multiplies the halo contribution to the lensing magnification distribution, and that the convolved log-normal and TurboGL shape is the true distribution.

Editorial extensions

If this is right

  • SN Ia lensing provides access to scales $k > 1\,h\,{\rm Mpc}^{-1}$ that galaxy shear surveys cut away, offering a probe of small-scale physics with a different systematic budget.
  • The measured $A_{\rm mod,S}=0.77^{+0.69}_{-0.40}$ is consistent with unity, so the current data do not distinguish between baryon feedback, neutrino mass, and non-standard dark matter models.
  • The near-zero correlation between $A_{\rm mod}$ and $S_8$ shows that SN lensing can separate small-scale power from linear growth; the paper notes a forecast that roughly 500,000 SNe Ia could constrain the amplitude to about 3% if likelihood systematics are controlled.
  • Coverage-probability validation indicates the 68% highest-density interval is conservative by about $\Delta A_{\rm mod}\simeq 0.19$, and the total systematic error is smaller than the statistical error by at least a factor of two.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate consistency test would be to measure $A_{\rm mod}$ from the cross-correlation of SN residuals with foreground galaxy density (as in the detection paper) and compare with the full-pdf value; disagreement would signal that a single rescaling factor is too simple.
  • Because $S_8$ and $A_{\rm mod}$ are nearly independent, combining SN lensing with galaxy shear and CMB lensing in a joint analysis could break the baryon-feedback/neutrino-mass degeneracy and constrain the shape of the small-scale power spectrum, not just its overall amplitude.
  • The posterior peak near $A_{\rm mod} = 0.30$, close to the prior edge, suggests that extending the prior toward smaller values or using a simulation-based likelihood on the current data could reveal whether the suppression preference is real or an artifact of truncation.
  • The paper's own estimate that reliable predictions require N-body simulations with particle masses near $10^7\,M_\odot$ suggests that such simulations, once available, would directly validate the halo-model magnification pdf and sharpen the physical interpretation of $A_{\rm mod}$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper presents a measurement of A_mod, an empirical scaling parameter of the halo contribution to the non-linear matter power spectrum, using the lensing magnification distribution of 1,484 SNe Ia from the Dark Energy Survey Year-5 sample. The lensing probability density is modelled as a convolution of a log-normal linear term and a TurboGL-based halo term (Eq. 7), with A_mod introduced as a scale parameter multiplying the halo contribution (Eq. 6). The main result is A_mod,S = 0.77^{+0.69}_{-0.40} (Eq. 16), consistent with unity but with the posterior peaking at low values, which the paper interprets as hints of power suppression on scales k > 1 h/Mpc. The analysis includes a likelihood validation on 240 SNANA simulations via expected coverage probability (Appendix A1), a systematic budget of Delta_A_mod = 0.21 (Appendix A4), and a robustness check against replacing CMB priors with DES+BAO priors.

Significance. If the model mapping is correct, this is the first supernova-based constraint on the non-linear matter power spectrum that is cleanly separated from linear-scale parameters such as sigma_8. The paper is generally honest about its limitations: it states that a reliable a-priori calculation of the magnification dispersion is unavailable, it validates the likelihood on simulations, and it provides a systematic budget that is smaller than the statistical error. However, the central interpretation depends critically on the relation between A_mod and the matter power spectrum, and the paper contains an internal inconsistency in that relation that must be resolved. The approach is promising and the data analysis is careful, but the current manuscript does not support its headline claim without clarification.

major comments (2)
  1. [Section 2.2, Eq. (6)] The definition of A_mod in Eq. (6) is a multiplicative factor on the halo power spectrum P_H, so the halo magnification dispersion should scale as sigma_H proportional to sqrt(A_mod). The text immediately after Eq. (7), however, states that 'A_mod is then a simple scale parameter on this pdf such that sigma_H(A_mod) = A_mod sigma_H(A_mod=1).' This is inconsistent: the stated scaling corresponds to P_H being multiplied by A_mod^2, not A_mod. If the implementation follows the stated linear scaling of sigma_H, then the parameter constrained by the data is the amplitude of the halo convergence field, and the implied power-spectrum multiplier is A_mod^2. The quoted result A_mod,S = 0.77 would then correspond to a suppression factor of ~0.59, with a considerably different credible interval after squaring, and the comparison with A_mod,I of Preston et al. (2023) would not be apples-to-apples. The ECP validation in Appendix A1 cannot detect this issue because the simulations are generated with the same (possibly mis-scaled) model. The authors must clarify which scaling is implemented. If the power-spectrum scaling of Eq. (6) is intended, the analysis must be re-run with sigma_H scaled as sqrt(A_mod); if the linear scaling is intended, the definition of A_mod and the interpretation of the result throughout the abstract and conclusions must be revised.
  2. [Section 5 and Appendix A1] The paper's central claim is that A_mod describes the suppression or enhancement of matter power on non-linear scales. This interpretation requires that the true response of the lensing magnification pdf to changes in small-scale power is faithfully represented by a single scale- and redshift-independent rescaling of the TurboGL halo term. The expected coverage tests in Appendix A1 validate the likelihood only against simulations generated with exactly this model, so they cannot establish that A_mod maps onto the physical power spectrum in the claimed way. The paper itself notes in Section 2.1 that a reliable a-priori calculation of sigma_Delta_m is unavailable and that emulators and simulations diverge strongly beyond k ~ 250 h/Mpc. To support the physical interpretation, the authors should either (a) validate the model against lensing maps or power spectra from simulations with varying small-scale power (e.g., different baryon feedback or dark matter models) and demonstrate that the A_mod rescaling captures the resulting change in the pdf, or (b) substantially soften the language in the abstract and conclusions to describe A_mod as an empirical shape parameter of the lensing pdf rather than a direct probe of the matter power spectrum.
minor comments (4)
  1. [Section 2.1] The sentence 'we emphasize that we do not make use of any of these models or Eqn. 5 in our analysis' is contradicted by Section 2.2, where Eq. (5) is used to obtain sigma_L for the linear log-normal term. Please correct this to state that the models and Eq. (5) are not used for the non-linear halo contribution.
  2. [Appendix A1] There is a typo in the line 'choose a credibile level' - 'credibile' should be 'credible'.
  3. [Figure 2 caption] The caption contains 'for aselection' which should be 'for a selection'.
  4. [Abstract] The phrase 'A_mod < 1.09 at 68% credibility' is a one-sided HPD interval, not a two-sided credible interval; consider rewording to 'the 68% highest-density interval is A_mod < 1.09' for clarity.

Circularity Check

1 steps flagged · score 4.0 of 10

A_mod is fit as a halo-pdf rescaling parameter, while its interpretation as a matter-power multiplier is an assumed identification; the quoted linear sigma-scaling is inconsistent with the quadratic power-spectrum integral.

  1. self definitional [Section 2.2, Eqs. (5)-(7)]
    "We write our power spectrum model as P(k,z)=P_L(k,z)+A_mod P_H(k,z) ... A_mod is then a simple scale parameter on this pdf such that sigma_H(A_mod)= A_mod sigma_H(A_mod=1)."

    By Eq. (5), sigma^2_Delta_m is an integral linear in P(k), so multiplying P_H by A_mod changes the halo contribution to sigma as sqrt(A_mod), not as A_mod. The likelihood as described uses the linear rescaling, making the fitted A_mod, by construction, a pdf-rescaling amplitude rather than the power-spectrum multiplier defined in Eq. (6). The abstract's reading of A_mod as 'the suppression or enhancement of matter power' is therefore an identification imposed by the scaling convention, not a derived consequence. If the code follows the quoted linear sigma_H scaling, the implied power-spectrum multiplier for A_mod,S=0.77 is A_mod^2 ~ 0.59, with a different credible interval after squaring, directly affecting the central interpretive claim.

full rationale

The central parameter estimation is not itself circular: A_mod is explicitly an empirical free parameter, and the posterior is a fit to DES-SN5YR data, not an out-of-sample prediction. The model choices (TurboGL, NFW profiles, Sheth et al. mass function) rest on external references plus prior work by the same authors, but those prior measurements are independent empirical results and the likelihood is internally validated with simulations, so the self-citations are not load-bearing. The paper also honestly states that a reliable a-priori calculation of sigma_Delta_m is unavailable and that Eq. (5) is used only for illustration. The dominant concern is instead the self-definitional step: the single place A_mod enters the likelihood is a linear rescaling of the halo pdf, which does not correspond to the linear-in-P_H meaning assigned in Eq. (6). This makes the physical interpretation of the constraint partially definitional rather than derived. The caveat is a serious consistency issue for the headline claim, but the data analysis itself is a standard parameter fit, so the circularity score is moderate rather than high.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central measurement rests on the TurboGL halo-model lensing pdf (NFW plus Sheth et al. 2001), the log-normal linear term, the scale-independent A_mod rescaling, and the sin-arcsin intrinsic model; the CMB prior defines the benchmark but does not force the result (S8-A_mod decorrelation in Figure 3). No invented physical entities. Free parameters: A_mod, the two intrinsic shape parameters, the SN absolute magnitude, and the 10^7 M_sun halo-mass cutoff.

free parameters (5)
  • A_mod = median 0.77; posterior peak 0.30; +0.69/-0.40 at 68%
    The empirical non-linear power amplitude and the central fitted quantity; constrained by the full shape of the SN residual distribution.
  • epsilon (intrinsic skew) = -0.07 (+0.04/-0.04)
    Sin-arcsin shape parameter fitted jointly with A_mod; required to separate redshift-dependent lensing skew from intrinsic skew.
  • delta (intrinsic kurtosis) = 0.91 (+0.06/-0.05)
    Sin-arcsin shape parameter fitted jointly with A_mod; controls the breadth of the intrinsic residual distribution.
  • SN Ia absolute magnitude M (degenerate with H0) = marginalized, not quoted
    Standard SN cosmology nuisance parameter; enters the distance modulus and is marginalized over using CMB-prior chains on H0.
  • Minimum halo mass for TurboGL integration = 10^7 M_sun
    Hand-chosen cutoff for the halo lensing integration; changes the absolute normalization of the halo pdf and therefore the scale of A_mod, though not fitted to the data.
assumptions (6)
  • domain assumption The lensing magnification pdf is the convolution of a log-normal linear-lensing distribution with the TurboGL halo-lensing distribution (Eq. 7).
    Underpins the entire likelihood; the log-normal form for the linear term is from Clerkin et al. (2017), and the convolution neglects correlations between the linear and halo contributions.
  • ad hoc to paper A_mod multiplies the halo power and pdf as a scale- and redshift-independent scalar (Eq. 6; sigma_H(A_mod) = A_mod sigma_H(1)).
    Defines what is measured; the paper gives no derivation that real power suppression or enhancement (baryon feedback, WDM, neutrinos) maps to a pure rescaling of the halo pdf.
  • domain assumption Dark matter haloes follow the Sheth et al. (2001) mass function refitted by Courtin et al. (2011), with NFW profiles, integrated down to 10^7 M_sun.
    TurboGL input; the Sheth-Tormen calibration is validated for CDM-only structure, but its extension to the small-scale lensing regime probed by SNe is assumed.
  • domain assumption Intrinsic SN Ia residual non-Gaussianity is redshift-independent and captured by the sin-arcsin family (Section 2.2).
    Needed to separate lensing skew (redshift-dependent) from intrinsic skew; stated as a presumption rather than tested against redshift-dependent intrinsic models.
  • standard math The benchmark A_mod = 1 corresponds to Flat-Lambda-CDM with Planck 2015 priors on A_s and Omega_m, n_s = 0.9665, tau = 0.0561, and sum m_nu = 0.06 eV.
    External input defining the baseline; all suppression claims are relative to this benchmark. Neutrino mass variations are deliberately absorbed into A_mod (Appendix A2).
  • domain assumption Compact objects contribute negligibly to SN lensing (alpha = Omega_CO/Omega_m < 0.12).
    Inherited from Shah et al. (2024a); if primordial black holes with alpha above about 0.12 existed, they would add a point-mass lensing component not captured by A_mod.

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Cite this review

Pith. "Pith review of It's not $\sigma_8$ : constraining the non-linear matter power spectrum with the Dark Energy Survey Year-5 supernova sample." pith.science (2026). https://pith.science/paper/BRVPJ4RJ

@misc{pith2026250119117,
  author       = {Pith},
  title        = {Pith review of: It's not $\sigma_8$ : constraining the non-linear matter power spectrum with the Dark Energy Survey Year-5 supernova sample},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BRVPJ4RJ}},
  note         = {Machine review of arXiv:2501.19117}
}
abstract

The weak gravitational lensing magnification of Type Ia supernovae (SNe Ia) is sensitive to the matter power spectrum on scales $k>1 h$ Mpc$^{-1}$, making it unwise to interpret SNe Ia lensing in terms of power on linear scales. We compute the probability density function of SNe Ia magnification as a function of standard cosmological parameters, plus an empirical parameter $A_{\rm mod}$ which describes the suppression or enhancement of matter power on non-linear scales compared to a cold dark matter only model. While baryons are expected to enhance power on the scales relevant to SN Ia lensing, other physics such as neutrino masses or non-standard dark matter may suppress power. Using the Dark Energy Survey Year-5 sample, we find $A_{\rm mod} = 0.77^{+0.69}_{-0.40}$ (68\% credible interval around the median). Although the median is consistent with unity there are hints of power suppression, with $A_{\rm mod} < 1.09$ at 68\% credibility.

Figures

Figures reproduced from arXiv: 2501.19117 by the authors.

Figure 1
Figure 1. The suppression or enhancement of the power spectrum compared to the dark matter only model of Mead et al. (2020). The models used are HMCODE2020 with 𝑇AGN = 8.0, the Cosmic-OWLS hydrodynamical simula￾tions (Le Brun et al. 2014), and the BAHAMAS hydrodynamical simulations (McCarthy et al. 2017). Power is suppressed on scales 0.1 < 𝑘/ℎ < 30 Mpc−1 by AGN and supernovae feedback prescriptions, which differ from model t… view at source ↗
Figure 2
Figure 2. The dispersion of lensing magnification derived from Eqn. 5 as a function of the integral cutoff 𝑘max with the lens at 𝑧𝑙 = 0.5 and the source at 𝑧𝑠 = 1.0, for a range of models and simulations of the matter power spectrum. The linear power spectrum is shown in yellow, the model of Mead et al. (2020) is shown without baryon feedback in magenta and with feedback in black Dotted and dashed magenta lines show the model… view at source ↗
Figure 3
Figure 3. A triangle plot of the posteriors for relevant model parameters, with the medians and 68% quantiles shown along the diagonal. The constraints on 𝑆8 and Ωm arise from the fit of the CMB power spectrum and SN Ia luminosity distances. The CMB priors we use are shown in red. As noted in the text, the Planck-lite-py likelihood used to generate the chains has moderately wider constraints than the full likelihood used in P… view at source ↗

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Works this paper leans on

85 extracted references · 14 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...

  2. [2]

    Abbott T. M. C., et al., 2022, @doi [ ] 10.1103/PhysRevD.105.023520 , https://ui.adsabs.harvard.edu/abs/2022PhRvD.105b3520A 105, 023520

    doi:10.1103/physrevd.105.023520 2022

  3. [3]

    Abdalla E., et al., 2022, @doi [Journal of High Energy Astrophysics] 10.1016/j.jheap.2022.04.002 , https://ui.adsabs.harvard.edu/abs/2022JHEAp..34...49A 34, 49

    doi:10.1016/j.jheap.2022.04.002 2022

  4. [4]

    Alam S., et al., 2021, @doi [ ] 10.1103/PhysRevD.103.083533 , https://ui.adsabs.harvard.edu/abs/2021PhRvD.103h3533A 103, 083533

    doi:10.1103/physrevd.103.083533 2021

  5. [5]

    Amon A., Efstathiou G., 2022, @doi [ ] 10.1093/mnras/stac2429 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.516.5355A 516, 5355

    doi:10.1093/mnras/stac2429 2022

  6. [6]

    E., Contreras S., Ondaro-Mallea L., Pellejero-Iba \ n ez M., Zennaro M., 2021, @doi [ ] 10.1093/mnras/stab1911 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.506.4070A 506, 4070

    Aric \`o G., Angulo R. E., Contreras S., Ondaro-Mallea L., Pellejero-Iba \ n ez M., Zennaro M., 2021, @doi [ ] 10.1093/mnras/stab1911 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.506.4070A 506, 4070

    doi:10.1093/mnras/stab1911 2021

  7. [7]

    Asgari M., et al., 2021, @doi [ ] 10.1051/0004-6361/202039070 , https://ui.adsabs.harvard.edu/abs/2021A&A...645A.104A 645, A104

    doi:10.1051/0004-6361/202039070 2021

  8. [8]

    Betoule M., et al., 2014, @doi [ ] 10.1051/0004-6361/201423413 , https://ui.adsabs.harvard.edu/abs/2014A&A...568A..22B 568, A22

    doi:10.1051/0004-6361/201423413 2014

Show all 85 references
  1. [9]

    Camilleri R., et al., 2024, @doi [ ] 10.1093/mnras/stae1988 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.tmp.1948C

    2024 doi

  2. [10]

    Castro T., Quartin M., 2014, @doi [ ] 10.1093/mnrasl/slu071 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.443L...6C 443, L6

    2014 doi

  3. [11]

    Clerkin L., et al., 2017, @doi [ ] 10.1093/mnras/stw2106 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.466.1444C 466, 1444

    2017 doi

  4. [12]

    M., Corasaniti P

    Courtin J., Rasera Y., Alimi J. M., Corasaniti P. S., Boucher V., F \"u zfa A., 2011, @doi [ ] 10.1111/j.1365-2966.2010.17573.x , https://ui.adsabs.harvard.edu/abs/2011MNRAS.410.1911C 410, 1911

    2011

  5. [13]

    DES Collaboration 2024, @doi [ ] 10.3847/2041-8213/ad6f9f , https://ui.adsabs.harvard.edu/abs/2024ApJ...973L..14A 973, L14

    2024 doi

  6. [14]

    arXiv:2404.03002

    DESI Collaboration 2024, @doi [arXiv e-prints] 10.48550/arXiv.2404.03002 , https://ui.adsabs.harvard.edu/abs/2024arXiv240403002D p. arXiv:2404.03002

    2024 doi arXiv

  7. [15]

    Dalal R., et al., 2023, @doi [ ] 10.1103/PhysRevD.108.123519 , https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l3519D 108, 123519

    2023 doi

  8. [16]

    Dark Energy Survey and Kilo-Degree Survey Collaboration 2023, @doi [The Open Journal of Astrophysics] 10.21105/astro.2305.17173 , https://ui.adsabs.harvard.edu/abs/2023OJAp....6E..36D 6, 36

    2023 arXiv

  9. [17]

    Darwish O., et al., 2021, @doi [ ] 10.1093/mnras/staa3438 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.500.2250D 500, 2250

    2021 doi

  10. [18]

    Efstathiou G., Gratton S., 2021, @doi [The Open Journal of Astrophysics] 10.21105/astro.1910.00483 , https://ui.adsabs.harvard.edu/abs/2021OJAp....4E...8E 4, 8

    2021 arXiv

  11. [19]

    R., Hearin A

    Eifler T., Krause E., Dodelson S., Zentner A. R., Hearin A. P., Gnedin N. Y., 2015, @doi [ ] 10.1093/mnras/stv2000 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.454.2451E 454, 2451

    2015 doi

  12. [20]

    arXiv:2406.18274

    Euclid Collaboration 2024, @doi [arXiv e-prints] 10.48550/arXiv.2406.18274 , https://ui.adsabs.harvard.edu/abs/2024arXiv240618274E p. arXiv:2406.18274

    2024 doi

  13. [21]

    Euclid Collaboration 2025, @doi [ ] 10.1051/0004-6361/202450859 , https://ui.adsabs.harvard.edu/abs/2025A&A...693A..58E 693, A58

    2025 doi

  14. [22]

    A., 1996, @doi [Comments on Astrophysics] 10.48550/arXiv.astro-ph/9608068 , https://ui.adsabs.harvard.edu/abs/1996ComAp..18..323F 18, 323

    Frieman J. A., 1996, @doi [Comments on Astrophysics] 10.48550/arXiv.astro-ph/9608068 , https://ui.adsabs.harvard.edu/abs/1996ComAp..18..323F 18, 323

    1996 doi arXiv

  15. [23]

    E., 2024, @doi [ ] 10.1088/1475-7516/2024/08/024 , https://ui.adsabs.harvard.edu/abs/2024JCAP...08..024G 2024, 024

    Garc \' a-Garc \' a C., Zennaro M., Aric \`o G., Alonso D., Angulo R. E., 2024, @doi [ ] 10.1088/1475-7516/2024/08/024 , https://ui.adsabs.harvard.edu/abs/2024JCAP...08..024G 2024, 024

    2024 doi

  16. [24]

    Handley W., 2019, @doi [The Journal of Open Source Software] 10.21105/joss.01414 , 4, 1414

    2019 doi

  17. [25]

    J., Hobson M

    Handley W. J., Hobson M. P., Lasenby A. N., 2015, @doi [ ] 10.1093/mnras/stv1911 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.453.4384H 453, 4384

    2015 doi

  18. [26]

    R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    Harris C. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    2020 doi

  19. [27]

    Hildebrandt H., et al., 2021, @doi [ ] 10.1051/0004-6361/202039018 , https://ui.adsabs.harvard.edu/abs/2021A&A...647A.124H 647, A124

    2021 doi

  20. [28]

    Hinton S., Brout D., 2020, @doi [Journal of Open Source Software] 10.21105/joss.02122 , 5, 2122

    2020 doi

  21. [29]

    D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    Hunter J. D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    2007 doi

  22. [30]

    C., Pewsey A., 2009, @doi [Biometrika] 10.1093/biomet/asp053 , 96, 761

    Jones M. C., Pewsey A., 2009, @doi [Biometrika] 10.1093/biomet/asp053 , 96, 761

    2009 doi

  23. [31]

    Kainulainen K., Marra V., 2009, @doi [ ] 10.1103/PhysRevD.80.123020 , https://ui.adsabs.harvard.edu/abs/2009PhRvD..80l3020K 80, 123020

    2009 doi

  24. [32]

    Kainulainen K., Marra V., 2011, @doi [ ] 10.1103/PhysRevD.84.063004 , https://ui.adsabs.harvard.edu/abs/2011PhRvD..84f3004K 84, 063004

    2011 doi

  25. [33]

    Kaiser N., 1984, @doi [ ] 10.1086/184341 , https://ui.adsabs.harvard.edu/abs/1984ApJ...284L...9K 284, L9

    1984 doi

  26. [34]

    Kannawadi A., et al., 2019, @doi [ ] 10.1051/0004-6361/201834819 , https://ui.adsabs.harvard.edu/abs/2019A&A...624A..92K 624, A92

    2019 doi

  27. [35]

    Kessler R., et al., 2009, , 121, 1028–1035

    2009

  28. [36]

    Le Brun A. M. C., McCarthy I. G., Schaye J., Ponman T. J., 2014, @doi [ ] 10.1093/mnras/stu608 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.441.1270L 441, 1270

    2014 doi

  29. [37]

    Lemos P., Cranmer M., Abidi M., Hahn C., Eickenberg M., Massara E., Yallup D., Ho S., 2023, @doi [Machine Learning: Science and Technology] 10.1088/2632-2153/acbb53 , https://ui.adsabs.harvard.edu/abs/2023MLS&T...4aLT01L 4, 01LT01

    2023 doi

  30. [38]

    Lewis A., Bridle S., 2002, @doi [ ] 10.1103/PhysRevD.66.103511 , https://ui.adsabs.harvard.edu/abs/2002PhRvD..66j3511L 66, 103511

    2002 doi

  31. [39]

    Li X., et al., 2023, @doi [ ] 10.1103/PhysRevD.108.123518 , https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l3518L 108, 123518

    2023 doi

  32. [40]

    Liu Y., et al., 2024, @doi [ ] 10.1093/mnras/stae003 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.52711740L 527, 11740

    2024 doi

  33. [41]

    Lu T., Haiman Z., 2021, @doi [ ] 10.1093/mnras/stab1978 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.506.3406L 506, 3406

    2021 doi

  34. [42]

    M., 2022, @doi [ ] 10.1093/mnras/stac161 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.1518L 511, 1518

    Lu T., Haiman Z., Zorrilla Matilla J. M., 2022, @doi [ ] 10.1093/mnras/stac161 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.1518L 511, 1518

    2022 doi

  35. [43]

    MacCrann N., et al., 2022, @doi [ ] 10.1093/mnras/stab2870 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.3371M 509, 3371

    2022 doi

  36. [44]

    M., Scovacricchi D., Bacon D., Collett T., Nichol R

    Macaulay E., Davis T. M., Scovacricchi D., Bacon D., Collett T., Nichol R. C., 2017, @doi [ ] 10.1093/mnras/stw3339 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.467..259M 467, 259

    2017 doi

  37. [45]

    Macaulay E., et al., 2020, @doi [ ] 10.1093/mnras/staa1852 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.496.4051M 496, 4051

    2020 doi

  38. [46]

    S., et al., 2024, @doi [ ] 10.3847/1538-4357/acff5f , https://ui.adsabs.harvard.edu/abs/2024ApJ...962..113M 962, 113

    Madhavacheril M. S., et al., 2024, @doi [ ] 10.3847/1538-4357/acff5f , https://ui.adsabs.harvard.edu/abs/2024ApJ...962..113M 962, 113

    2024 doi

  39. [47]

    V., Wechsler R

    Mandelbaum R., Tasitsiomi A., Seljak U., Kravtsov A. V., Wechsler R. H., 2005, @doi [ ] 10.1111/j.1365-2966.2005.09417.x , https://ui.adsabs.harvard.edu/abs/2005MNRAS.362.1451M 362, 1451

    2005

  40. [48]

    Mandelbaum R., et al., 2018, @doi [ ] 10.1093/mnras/sty2420 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.481.3170M 481, 3170

    2018 doi

  41. [49]

    Marra V., Quartin M., Amendola L., 2013, @doi [ ] 10.1103/PhysRevD.88.063004 , https://ui.adsabs.harvard.edu/abs/2013PhRvD..88f3004M 88, 063004

    2013 doi

  42. [50]

    G., Schaye J., Bird S., Le Brun A

    McCarthy I. G., Schaye J., Bird S., Le Brun A. M. C., 2017, @doi [ ] 10.1093/mnras/stw2792 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.465.2936M 465, 2936

    2017 doi

  43. [51]

    J., Heymans C., Lombriser L., Peacock J

    Mead A. J., Heymans C., Lombriser L., Peacock J. A., Steele O. I., Winther H. A., 2016, @doi [ ] 10.1093/mnras/stw681 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.459.1468M 459, 1468

    2016 doi

  44. [52]

    J., Tr \"o ster T., Heymans C., Van Waerbeke L., McCarthy I

    Mead A. J., Tr \"o ster T., Heymans C., Van Waerbeke L., McCarthy I. G., 2020, @doi [ ] 10.1051/0004-6361/202038308 , https://ui.adsabs.harvard.edu/abs/2020A&A...641A.130M 641, A130

    2020 doi

  45. [53]

    J., Brieden S., Tr \"o ster T., Heymans C., 2021, @doi [ ] 10.1093/mnras/stab082 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.1401M 502, 1401

    Mead A. J., Brieden S., Tr \"o ster T., Heymans C., 2021, @doi [ ] 10.1093/mnras/stab082 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.1401M 502, 1401

    2021 doi

  46. [54]

    Y., 2018, @doi [ ] 10.3847/1538-4357/aad3b1 , https://ui.adsabs.harvard.edu/abs/2018ApJ...863..173M 863, 173

    Mohammed I., Gnedin N. Y., 2018, @doi [ ] 10.3847/1538-4357/aad3b1 , https://ui.adsabs.harvard.edu/abs/2018ApJ...863..173M 863, 173

    2018 doi

  47. [55]

    M \"o ller A., de Boissi \`e re T., 2020, @doi [ ] 10.1093/mnras/stz3312 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.4277M 491, 4277

    2020 doi

  48. [56]

    M \"o ller A., et al., 2022, @doi [ ] 10.1093/mnras/stac1691 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.514.5159M 514, 5159

    2022 doi

  49. [57]

    Myles J., et al., 2021, @doi [ ] 10.1093/mnras/stab1515 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.4249M 505, 4249

    2021 doi

  50. [58]

    F., Frenk C

    Navarro J. F., Frenk C. S., White S. D. M., 1997, @doi [ ] 10.1086/304888 , https://ui.adsabs.harvard.edu/abs/1997ApJ...490..493N 490, 493

    1997 doi

  51. [59]

    Pan Z., et al., 2023, @doi [ ] 10.1103/PhysRevD.108.122005 , https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l2005P 108, 122005

    2023 doi

  52. [60]

    D., 2024, @doi [The Open Journal of Astrophysics] 10.33232/001c.117419 , https://ui.adsabs.harvard.edu/abs/2024OJAp....7E..34P 7, 34

    Paopiamsap A., Porqueres N., Alonso D., Harnois-Deraps J., Leonard C. D., 2024, @doi [The Open Journal of Astrophysics] 10.33232/001c.117419 , https://ui.adsabs.harvard.edu/abs/2024OJAp....7E..34P 7, 34

    2024 doi

  53. [61]

    Planck Collaboration 2020a, @doi [ ] 10.1051/0004-6361/201833910 , https://ui.adsabs.harvard.edu/abs/2020A&A...641A...6P 641, A6

    doi

  54. [62]

    Planck Collaboration 2020b, @doi [ ] 10.1051/0004-6361/201833886 , https://ui.adsabs.harvard.edu/abs/2020A&A...641A...8P 641, A8

    doi

  55. [63]

    Preston C., Amon A., Efstathiou G., 2023, @doi [ ] 10.1093/mnras/stad2573 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.525.5554P 525, 5554

    2023 doi

  56. [64]

    Prince H., Dunkley J., 2019, @doi [ ] 10.1103/PhysRevD.100.083502 , https://ui.adsabs.harvard.edu/abs/2019PhRvD.100h3502P 100, 083502

    2019 doi

  57. [65]

    Qu H., Sako M., M \"o ller A., Doux C., 2021, @doi [ ] 10.3847/1538-3881/ac0824 , https://ui.adsabs.harvard.edu/abs/2021AJ....162...67Q 162, 67

    2021 doi

  58. [66]

    Qu H., et al., 2024, @doi [ ] 10.3847/1538-4357/ad251d , https://ui.adsabs.harvard.edu/abs/2024ApJ...964..134Q 964, 134

    2024 doi

  59. [67]

    Quartin M., Marra V., Amendola L., 2014, @doi [ ] 10.1103/PhysRevD.89.023009 , https://ui.adsabs.harvard.edu/abs/2014PhRvD..89b3009Q 89, 023009

    2014 doi

  60. [68]

    arXiv:2311.12098

    Rubin D., et al., 2023, @doi [arXiv e-prints] 10.48550/arXiv.2311.12098 , https://ui.adsabs.harvard.edu/abs/2023arXiv231112098R p. arXiv:2311.12098

    2023 doi arXiv

  61. [69]

    O., et al., 2024, @doi [ ] 10.3847/1538-4357/ad739a , https://ui.adsabs.harvard.edu/abs/2024ApJ...975....5S 975, 5

    S \'a nchez B. O., et al., 2024, @doi [ ] 10.3847/1538-4357/ad739a , https://ui.adsabs.harvard.edu/abs/2024ApJ...975....5S 975, 5

    2024 doi

  62. [70]

    Schneider A., Teyssier R., 2015, @doi [ ] 10.1088/1475-7516/2015/12/049 , https://ui.adsabs.harvard.edu/abs/2015JCAP...12..049S 2015, 049

    2015 doi

  63. [71]

    E., Le Brun A

    Schneider A., Teyssier R., Stadel J., Chisari N. E., Le Brun A. M. C., Amara A., Refregier A., 2019, @doi [ ] 10.1088/1475-7516/2019/03/020 , https://ui.adsabs.harvard.edu/abs/2019JCAP...03..020S 2019, 020

    2019 doi

  64. [72]

    arXiv:2410.07956

    Shah P., et al., 2024a, @doi [arXiv e-prints] 10.48550/arXiv.2410.07956 , https://ui.adsabs.harvard.edu/abs/2024arXiv241007956S p. arXiv:2410.07956

    doi arXiv

  65. [73]

    Shah P., et al., 2024b, @doi [ ] 10.1093/mnras/stae1515 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.532..932S 532, 932

    doi

  66. [74]

    K., Mo H

    Sheth R. K., Mo H. J., Tormen G., 2001, @doi [ ] 10.1046/j.1365-8711.2001.04006.x , https://ui.adsabs.harvard.edu/abs/2001MNRAS.323....1S 323, 1

    2001

  67. [75]

    E., et al., 2003, @doi [ ] 10.1046/j.1365-8711.2003.06503.x , https://ui.adsabs.harvard.edu/abs/2003MNRAS.341.1311S 341, 1311

    Smith R. E., et al., 2003, @doi [ ] 10.1046/j.1365-8711.2003.06503.x , https://ui.adsabs.harvard.edu/abs/2003MNRAS.341.1311S 341, 1311

    2003

  68. [76]

    Sullivan M., et al., 2006, @doi [ ] 10.1086/506137 , https://ui.adsabs.harvard.edu/abs/2006ApJ...648..868S 648, 868

    2006 doi

  69. [77]

    Takahashi R., Sato M., Nishimichi T., Taruya A., Oguri M., 2012, @doi [ ] 10.1088/0004-637X/761/2/152 , https://ui.adsabs.harvard.edu/abs/2012ApJ...761..152T 761, 152

    2012 doi

  70. [78]

    arXiv:2403.20323

    Terasawa R., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2403.20323 , https://ui.adsabs.harvard.edu/abs/2024arXiv240320323T p. arXiv:2403.20323

    2024 doi arXiv

  71. [79]

    Vincenzi M., et al., 2024, @doi [ ] 10.3847/1538-4357/ad5e6c , https://ui.adsabs.harvard.edu/abs/2024ApJ...975...86V 975, 86

    2024 doi

  72. [80]

    Virtanen P., et al., 2020, @doi [Nature Methods] 10.1038/s41592-019-0686-2 , https://rdcu.be/b08Wh 17, 261

    2020 doi

  73. [81]

    S., Gao L., Jenkins A., Springel V., White S

    Wang J., Bose S., Frenk C. S., Gao L., Jenkins A., Springel V., White S. D. M., 2020, @doi [ ] 10.1038/s41586-020-2642-9 , https://ui.adsabs.harvard.edu/abs/2020Natur.585...39W 585, 39

    2020 doi

  74. [82]

    H., Jing Y

    Zhao D. H., Jing Y. P., Mo H. J., B \"o rner G., 2009, @doi [ ] 10.1088/0004-637X/707/1/354 , https://ui.adsabs.harvard.edu/abs/2009ApJ...707..354Z 707, 354

    2009 doi

  75. [83]

    S., Gao L., Jenkins A., Liao S., Liu Y., Wang J., 2024, @doi [ ] 10.1093/mnras/stae289 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.7300Z 528, 7300

    Zheng H., Bose S., Frenk C. S., Gao L., Jenkins A., Liao S., Liu Y., Wang J., 2024, @doi [ ] 10.1093/mnras/stae289 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.7300Z 528, 7300

    2024 doi

  76. [84]

    Zumalac \'a rregui M., Seljak U., 2018, @doi [ ] 10.1103/PhysRevLett.121.141101 , https://ui.adsabs.harvard.edu/abs/2018PhRvL.121n1101Z 121, 141101

    2018 doi

  77. [85]

    P., McCarthy I

    van Daalen M. P., McCarthy I. G., Schaye J., 2020, @doi [ ] 10.1093/mnras/stz3199 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.2424V 491, 2424

    2020 doi

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