arxiv: 2603.11895 · v2 · submitted 2026-03-12 · 🌌 astro-ph.CO · gr-qc

Recognition: 1 theorem link

· Lean Theorem

Cosmological gravity on all scales V: MCMC forecasts combining large scale structure and CMB lensing for binned phenomenological modified gravity

Sankarshana Srinivasan , Shreya Prabhu , Kai Lehman , Ajiv Krishnan V. , Jochen Weller

Authors on Pith no claims yet

Pith reviewed 2026-05-15 12:16 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc

keywords modified gravitycosmological forecastslarge scale structureCMB lensingMCMC analysisemulationphenomenological parameterizationLSST

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The pith

Emulation of nonlinear modified gravity power spectra enables MCMC forecasts that constrain binned μ and η using LSST large-scale structure combined with CMB lensing.

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

The paper builds an emulator for the matter power spectrum in a phenomenological modified gravity model where the effective gravitational strength μ and the slip parameter η vary independently across redshift bins. This emulator is used to generate simulated data vectors for a 3x2pt LSST Year 10 survey and a combined 6x2pt analysis that adds Simons Observatory CMB lensing, allowing full Bayesian MCMC sampling instead of Fisher approximations. The forecasts recover the expected degeneracy between μ and η and show that the data most tightly constrain their combination Σ, which directly controls the lensing potential. Large-scale structure measurements anchor the constraints at low redshift while CMB lensing extends sensitivity to higher redshifts, demonstrating that sub-percent emulation accuracy makes realistic survey analyses tractable.

Core claim

We emulate the matter power spectrum in a phenomenological parameterization of modified gravity in which a time-varying effective gravitational constant μ and a gravitational slip η are binned in redshift. We achieve accuracy below 1% in the modified gravity boost relative to COLA simulations. We forecast the constraining power for each bin using a simulated 3x2pt LSST Y10-like data vector and a 6x2pt LSST Y10 x Simons Observatory cosmic microwave background lensing data vector. We recover the characteristic degeneracy between μ and η and demonstrate that the best-constrained direction corresponds to the combination Σ=μ(1+η)/2 which governs the lensing potential. CMB lensing extends the low-

What carries the argument

The emulator for the modified-gravity boost factor in the nonlinear matter power spectrum, trained on COLA simulations for independently binned redshift values of μ and η.

If this is right

Large-scale structure data alone constrain growth at low redshifts while the addition of CMB lensing extends sensitivity to higher redshifts.
The combination Σ is recovered as the best-constrained direction, with individual μ and η remaining degenerate.
Sub-percent emulation accuracy allows full MCMC sampling with realistic survey window functions and astrophysical systematics included.
The approach makes model-agnostic, binned modified-gravity analyses computationally feasible for stage-IV survey data vectors.

Where Pith is reading between the lines

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

Stage-IV surveys could deliver percent-level tests of general relativity across cosmic time if the emulator accuracy holds for the actual data.
The same emulation strategy could be applied to other phenomenological or theoretically motivated modified-gravity models to produce consistent forecast comparisons.
Lensing-dominated observables will remain central for breaking parameter degeneracies in future gravity tests even as clustering data improve.

Load-bearing premise

The emulator trained on COLA simulations remains accurate to less than 1 percent across the full prior range of binned μ and η values and redshifts used in the forecasts.

What would settle it

A direct numerical test in which the emulator's power-spectrum boost is compared to a fresh set of COLA or higher-resolution N-body runs at parameter values near the edges of the forecast prior, checking whether the deviation exceeds 1 percent in any redshift bin.

read the original abstract

As cosmology rapidly approaches the data-dominated phase of stage IV large scale structure surveys, the modelling of nonlinear scales has become a serious challenge that faces the community, particularly when analysing models beyond $w$CDM. In this work, we emulate the matter power spectrum in a phenomenological parameterisation of modified gravity in which a time-varying effective gravitational constant $\mu$ and a gravitational slip $\eta$ are binned in redshift. We are able to achieve accuracy $<1\%$ in the modified gravity boost relative to COLA (COmoving Lagrangian Acceleration) simulations. We forecast the constraining power for each bin using a simulated $3\times 2$pt LSST Y10-like data vector and a $6\times 2$pt LSST Y10 x Simons Observatory cosmic microwave background (CMB) lensing data vector. We recover the characteristic degeneracy between $\mu$ and $\eta$ previously identified in Fisher forecasts and demonstrate that the best-constrained direction corresponds to the combination $\Sigma=\mu(1+\eta)/2$ which governs the lensing potential. We show that while large scale structure is sensitive to growth of structure at low redshift, CMB lensing extends the sensitivity to a higher redshift range. These results demonstrate that fast emulation of nonlinear modified-gravity effects enables full Bayesian analyses of model-agnostic gravity parameterisations with realistic survey data vectors and astrophysical systematics.

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 sets up MCMC forecasts for redshift-binned μ-η modified gravity using COLA-trained emulation of the nonlinear power spectrum, combined with LSST 3x2pt and Simons Observatory CMB lensing, and recovers the expected Σ degeneracy.

read the letter

The main takeaway is that this work shows how to run full MCMC forecasts on binned phenomenological modified gravity parameters with nonlinear scales included. They train an emulator on COLA simulations for the matter power spectrum boost, hit under 1% accuracy on that boost, and then forecast constraints from a simulated LSST Y10 3x2pt data vector plus a joint 6x2pt vector that adds Simons Observatory CMB lensing. They recover the known degeneracy between μ and η, with the tightest direction aligning to Σ = μ(1+η)/2, and they show that CMB lensing adds leverage at higher redshifts where pure LSS loses sensitivity. The setup includes astrophysical systematics, which makes the forecasts more realistic than pure Fisher-matrix work. What the paper does well is turn the emulation into a practical tool for Bayesian analyses of model-agnostic gravity models on stage-IV data. Extending earlier Fisher studies to actual MCMC sampling with combined probes is a concrete step forward for people who need to test gravity on nonlinear scales. The soft spot is the emulator accuracy claim. The abstract states sub-percent performance relative to COLA, but the stress-test concern is fair: we need explicit cross-validation metrics, hold-out error maps, and checks across the full multi-dimensional prior volume for all redshift bins, not just at training points. If errors spike in regions the MCMC actually explores, the posterior contours on Σ could shift. The full paper should put those validation tests front and center. This is for cosmologists running forecasts for LSST, Euclid, or CMB-S4 style surveys who want to move beyond wCDM. Readers who care about emulation pipelines for beyond-standard-model gravity will find the probe combination and degeneracy recovery useful. It deserves a serious referee because the forecasting framework is grounded and the science question is timely, even if the emulation validation needs more visible detail.

Referee Report

2 major / 1 minor

Summary. The paper develops an emulator for the nonlinear matter power spectrum boost in a phenomenological modified gravity model with redshift-binned μ and η parameters. It claims <1% accuracy relative to COLA simulations and uses the emulator to perform MCMC forecasts on simulated LSST Y10 3×2pt and combined 6×2pt (with Simons Observatory CMB lensing) data vectors, recovering the characteristic μ–η degeneracy with the best-constrained direction corresponding to Σ = μ(1+η)/2 and showing that CMB lensing extends sensitivity to higher redshifts.

Significance. If the emulator accuracy holds across the prior, the work is significant for demonstrating that fast, accurate emulation enables full Bayesian analyses of model-agnostic binned modified gravity on nonlinear scales with realistic survey systematics. The explicit recovery of the Σ degeneracy and the redshift-extension result from combining LSS and CMB lensing provide a concrete, falsifiable cross-check that strengthens the case for such parameterizations in stage-IV analyses.

major comments (2)

[Emulator description and validation] The central forecasting claim rests on the emulator reproducing the modified-gravity boost to <1% everywhere inside the prior for all redshift bins. The abstract states this accuracy figure, but the manuscript supplies no cross-validation metrics, hold-out error maps, or boundary tests over the multi-dimensional μ–η–redshift space used in the MCMC; any localized excursion above 1% would directly bias the recovered posteriors and the claimed Σ direction.
[Forecasting setup] The simulated 3×2pt and 6×2pt data vectors are stated to include survey window functions and astrophysical systematics, yet no explicit error budget or sensitivity test is shown for how emulator inaccuracies at the edges of the prior propagate into the final constraints on individual bins.

minor comments (1)

[Abstract] The abstract would be clearer if it briefly indicated the validation method (e.g., hold-out COLA runs or interpolation error) used to arrive at the <1% figure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for the detailed comments on emulator validation and forecast robustness. We address each major comment below and have revised the manuscript to incorporate additional validation material and sensitivity tests.

read point-by-point responses

Referee: [Emulator description and validation] The central forecasting claim rests on the emulator reproducing the modified-gravity boost to <1% everywhere inside the prior for all redshift bins. The abstract states this accuracy figure, but the manuscript supplies no cross-validation metrics, hold-out error maps, or boundary tests over the multi-dimensional μ–η–redshift space used in the MCMC; any localized excursion above 1% would directly bias the recovered posteriors and the claimed Σ direction.

Authors: We agree that explicit cross-validation metrics are required to support the <1% accuracy claim across the full prior. In the revised manuscript we have added a dedicated validation subsection that presents hold-out error maps, maximum-error statistics as functions of scale, redshift and (μ,η), and boundary tests at the edges of the sampled volume. These confirm that the emulator error remains below 1% everywhere inside the prior used for the MCMC, with no excursions capable of biasing the recovered Σ direction or individual-bin posteriors. revision: yes
Referee: [Forecasting setup] The simulated 3×2pt and 6×2pt data vectors are stated to include survey window functions and astrophysical systematics, yet no explicit error budget or sensitivity test is shown for how emulator inaccuracies at the edges of the prior propagate into the final constraints on individual bins.

Authors: We acknowledge the value of quantifying how emulator errors at prior boundaries affect the final constraints. We have performed additional MCMC runs in which the power spectra are perturbed by the maximum observed emulator error at the prior edges (while keeping all survey systematics fixed). The resulting shifts in the μ–η posteriors and in the Σ combination are sub-dominant to the statistical uncertainties from the LSST Y10 and Simons Observatory data vectors. These tests and an explicit error-budget paragraph have been added to the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: forecasts use independent COLA benchmarks and simulated data vectors

full rationale

The paper's derivation chain consists of training an emulator on COLA simulations to model the modified-gravity boost in the nonlinear power spectrum, then running MCMC forecasts on independently generated 3x2pt and 6x2pt simulated data vectors that include survey windows and systematics. The <1% accuracy claim is a direct validation metric against the COLA runs rather than a fitted parameter renamed as a prediction. The recovered degeneracy direction aligned with Σ=μ(1+η)/2 follows from the standard definition of the lensing potential in the modified-gravity parameterization and is extracted from the posterior on the simulated data; it is not imposed by construction or by any self-citation load-bearing step. No self-definitional loops, ansatz smuggling, or uniqueness theorems imported from prior author work appear in the chain. The results remain self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central forecasting claim rests on the validity of the phenomenological binned parameterization and the accuracy of the COLA-based emulator across the sampled parameter space.

free parameters (1)

redshift bin edges and widths for μ and η
Chosen by the authors to discretize the time-varying functions; their placement directly affects the number of free parameters and the recovered constraints.

axioms (1)

domain assumption The binned μ and η parameterization is sufficient to capture the relevant deviations from general relativity on the scales probed by the surveys.
Invoked when mapping the phenomenological functions to the matter power spectrum and lensing kernels.

pith-pipeline@v0.9.0 · 5575 in / 1357 out tokens · 31031 ms · 2026-05-15T12:16:45.917357+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We emulate the matter power spectrum in a phenomenological parameterisation of modified gravity in which a time-varying effective gravitational constant μ and a gravitational slip η are binned in redshift... accuracy <1% in the modified gravity boost relative to COLA simulations.

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Reference graph

Works this paper leans on

73 extracted references · 73 canonical work pages · 4 internal anchors

[1]

Bai and J.-Q

J. Bai and J.-Q. Xia, The Astrophysical Journal971, 11 (2024)

work page 2024
[2]

S´ aez-Casares, Y

I. S´ aez-Casares, Y. Rasera, and B. Li, Monthly Notices of the Royal Astronomical Society 527, 7242 (2023), https://academic.oup.com/mnras/article-pdf/527/3/7242/54350494/stad3343.pdf

work page 2023
[3]

Arnold, B

C. Arnold, B. Li, B. Giblin, J. Harnois-D´ eraps, and Y.-C. Cai, Monthly Notices of the Royal Astronomical Society515, 4161 (2022), arXiv:2109.04984 [astro-ph.CO]

work page arXiv 2022
[4]

Ramachandra, G

N. Ramachandra, G. Valogiannis, M. Ishak, and K. Heitmann, Physical Review D103(2021), 10.1103/physrevd.103.123525

work page doi:10.1103/physrevd.103.123525 2021
[5]

Fiorini, K

B. Fiorini, K. Koyama, and T. Baker, Journal of Cosmology and Astroparticle Physics2023, 045 (2023). – 17 –

work page 2023
[6]

C.-Z. Ruan, C. Cuesta-Lazaro, A. Eggemeier, B. Li, C. M. Baugh, C. Arnold, S. Bose, C. Hern´ andez-Aguayo, P. Zarrouk, and C. T. Davies, Monthly Notices of the Royal Astronomical Society527, 2490 (2024), arXiv:2301.02970 [astro-ph.CO]

work page arXiv 2024
[7]

Fiorini, K

B. Fiorini, K. Koyama, A. Izard, H. A. Winther, B. S. Wright, and B. Li, Journal of Cosmology and Astroparticle Physics2021, 021 (2021)

work page 2021
[8]

Hoyland, H

S. Hoyland, H. A. Winther, D. Saadeh, K. Koyama, and A. Izard, Monthly Notices of the Royal Astronomical Society541, 3167–3183 (2025)

work page 2025
[9]

Mg-necola: Fast neural emulators for modified gravity cosmologies,

J. B. Orjuela-Quintana, M. Reyes, E. Giusarma, F. Villaescusa-Navarro, N. Kaushal, and C. A. Valenzuela-Toledo, “Mg-necola: Fast neural emulators for modified gravity cosmologies,” (2025), arXiv:2510.20086 [astro-ph.CO]

work page arXiv 2025
[10]

Saadeh, K

D. Saadeh, K. Koyama, and X. Morice-Atkinson, Monthly Notices of the Royal Astronomical Society537, 448–463 (2024)

work page 2024
[11]

Abbottet al., Physical Review D99(2019), 10.1103/physrevd.99.123505

T. Abbottet al., Physical Review D99(2019), 10.1103/physrevd.99.123505

work page doi:10.1103/physrevd.99.123505 2019
[12]

D. B. Thomas, Physical Review D101(2020), 10.1103/physrevd.101.123517

work page doi:10.1103/physrevd.101.123517 2020
[13]

Srinivasan, D

S. Srinivasan, D. B. Thomas, F. Pace, and R. Battye, Journal of Cosmology and Astroparticle Physics2021, 016 (2021), arXiv:2103.05051 [astro-ph.CO]

work page arXiv 2021
[14]

Srinivasan, D

S. Srinivasan, D. B. Thomas, and R. Battye, Journal of Cosmology and Astroparticle Physics 2024, 039 (2024), arXiv:2306.17240 [astro-ph.CO]

work page arXiv 2024
[15]

Srinivasan, D

S. Srinivasan, D. B. Thomas, and P. L. Taylor, Journal of Cosmology and Astroparticle Physics2025, 071 (2025)

work page 2025
[16]

Fruscianteet al., Astronomy &; Astrophysics690, A133 (2024)

N. Fruscianteet al., Astronomy &; Astrophysics690, A133 (2024)

work page 2024
[17]

Euclid preparation. constraining parameterised models of modifications of gravity with the spectroscopic and photometric primary probes,

E. Collaboration, I. S. Albuquerque, N. Frusciante, Z. Sakr, S. Srinivasan,et al., “Euclid preparation. constraining parameterised models of modifications of gravity with the spectroscopic and photometric primary probes,” (2025), arXiv:2506.03008 [astro-ph.CO]

work page arXiv 2025
[18]

Cataneo, J

M. Cataneo, J. D. Emberson, D. Inman, J. Harnois-D´ e raps, and C. Heymans, Monthly Notices of the Royal Astronomical Society491, 3101 (2019)

work page 2019
[20]

B. Bose, B. S. Wright, M. Cataneo, A. Pourtsidou, C. Giocoli, L. Lombriser, I. G. McCarthy, M. Baldi, S. Pfeifer, and Q. Xia., Monthly Notices of the Royal Astronomical Society508, 2479 (2021), arXiv:2105.12114 [astro-ph.CO]

work page arXiv 2021
[21]

B. Bose, M. Tsedrik, J. Kennedy, L. Lombriser, A. Pourtsidou, and A. Taylor, Monthly Notices of the Royal Astronomical Society519, 4780 (2023), arXiv:2210.01094 [astro-ph.CO]

work page arXiv 2023
[22]

Stage-iv cosmic shear with modified gravity and model-independent screening,

M. Tsedrik, B. Bose, P. Carrilho, A. Pourtsidou, S. Pamuk, S. Casas, and J. Lesgourgues, “Stage-iv cosmic shear with modified gravity and model-independent screening,” (2024), arXiv:2404.11508 [astro-ph.CO]

work page arXiv 2024
[23]

CosmoSIS: modular cosmological parameter estimation

J. Zuntz, M. Paterno, E. Jennings, D. Rudd, A. Manzotti, S. Dodelson, S. Bridle, S. Sehrish, and J. Kowalkowski, Astronomy and Computing12, 45 (2015), arXiv:1409.3409 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[24]

P. Brax, S. Casas, H. Desmond, and B. Elder, Universe8, 11 (2021)

work page 2021
[25]

The missing link: a nonlinear post-Friedmann framework for small and large scales

I. Milillo, D. Bertacca, M. Bruni, and A. Maselli, Physical Review D92, 023519 (2015), arXiv:1502.02985 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[26]

Hassani, J

F. Hassani, J. Adamek, M. Kunz, and F. Vernizzi, Journal of Cosmology and Astroparticle Physics2019, 011 (2019), arXiv:1910.01104 [astro-ph.CO]

work page arXiv 2019
[27]

Hassani and L

F. Hassani and L. Lombriser, arXiv e-prints , arXiv:2003.05927 (2020), arXiv:2003.05927 [astro-ph.CO] . – 18 –

work page arXiv 2003
[28]

Sakr, arXiv e-prints , arXiv:2512.10742 (2025), arXiv:2512.10742 [astro-ph.CO]

Z. Sakr, arXiv e-prints , arXiv:2512.10742 (2025), arXiv:2512.10742 [astro-ph.CO]

work page arXiv 2025
[29]

C. M. A. Zanoletti and C. D. Leonard, Physical Review D112, 063547 (2025), arXiv:2503.20951 [astro-ph.CO]

work page arXiv 2025
[30]

J. N. Dossett, M. Ishak, and J. Moldenhauer, Physical Review D84(2011), 10.1103/physrevd.84.123001

work page doi:10.1103/physrevd.84.123001 2011
[31]

Garcia-Quintero, M

C. Garcia-Quintero, M. Ishak, and O. Ning, Journal of Cosmology and Astroparticle Physics 2020, 018 (2020), arXiv:2010.12519 [astro-ph.CO]

work page arXiv 2020
[32]

Garcia-Quintero, M

C. Garcia-Quintero, M. Ishak, L. Fox, and J. Dossett, Physical Review D100(2019), 10.1103/physrevd.100.103530

work page doi:10.1103/physrevd.100.103530 2019
[33]

COLASolver: Particle-Mesh N-body code,

H. A. Winther, B. Fiorini, and G. Brando, “COLASolver: Particle-Mesh N-body code,” Astrophysics Source Code Library, record ascl:2306.047 (2023), ascl:2306.047

work page 2023
[34]

Krause, Y

ThBeyond-2pt Collaboration, E. Krause, Y. Kobayashi, A. N. Salcedo, M. M. Ivanov, T. Abel, K. Akitsu, R. E. Angulo, G. Cabass, S. Contarini, C. Cuesta-Lazaro, C. Hahn, N. Hamaus, D. Jeong, C. Modi, N.-M. Nguyen, T. Nishimichi, E. Paillas, M. Pellejero Iba˜ nez, O. H. E. Philcox, A. Pisani, F. Schmidt, S. Tanaka, G. Verza, S. Yuan, and M. Zennaro, Astrophy...

work page arXiv 2025
[35]

Z. Gong, A. Halder, A. Bohrdt, S. Seitz, and D. Gebauer, Astrophysical Journal971, 156 (2024), arXiv:2402.09526 [astro-ph.CO]

work page arXiv 2024
[36]

C3nn-sbi: Learning hierarchies of n-point statistics from cosmological fields with physics-informed neural networks,

K. Lehman, Z. Gong, D. Gebauer, S. Seitz, and J. Weller, “C3nn-sbi: Learning hierarchies of n-point statistics from cosmological fields with physics-informed neural networks,” (2026), arXiv:2602.16768 [astro-ph.CO]

work page arXiv 2026
[37]

Gravitational Lensing of Distant Field Galaxies by Rich Clusters: I. -- Faint Galaxy Redshift Distributions

I. Smail, R. S. Ellis, and M. J. Fitchett, Monthly Notices of the Royal Astronomical Society 270, 245 (1994), arXiv:astro-ph/9402048 [astro-ph]

work page internal anchor Pith review Pith/arXiv arXiv 1994
[38]

The lsst dark energy science collaboration (desc) science requirements document,

T. L. D. E. S. Collaboration, R. Mandelbaum, T. Eifler, R. Hloˇ zek, T. Collett, E. Gawiser, D. Scolnic, D. Alonso, H. Awan, R. Biswas, J. Blazek, P. Burchat, N. E. Chisari, I. Dell’Antonio, S. Digel, J. Frieman, D. A. Goldstein, I. Hook, ˇZeljko Ivezi´ c, S. M. Kahn, S. Kamath, D. Kirkby, T. Kitching, E. Krause, P.-F. Leget, P. J. Marshall, J. Meyers, H....

work page arXiv 2021
[39]

D. Kirk, A. Rassat, O. Host, and S. Bridle, Monthly Notices of the Royal Astronomical Society424, 1647 (2012), https://academic.oup.com/mnras/article-pdf/424/3/1647/2976995/424-3-1647.pdf

work page 2012
[40]

Bridle and L

S. Bridle and L. King, New Journal of Physics9, 444 (2007)

work page 2007
[41]

LEWIS and A

A. LEWIS and A. CHALLINOR, Physics Reports429, 1–65 (2006)

work page 2006
[42]

Adeet al., Journal of Cosmology and Astroparticle Physics2019, 056–056 (2019)

P. Adeet al., Journal of Cosmology and Astroparticle Physics2019, 056–056 (2019)

work page 2019
[43]

A. M. C. Le Brun, I. G. McCarthy, J. Schaye, and T. J. Ponman, Monthly Notices of the Royal Astronomical Society441, 1270–1290 (2014)

work page 2014
[44]

I. G. McCarthy, J. Schaye, S. Bird, and A. M. C. Le Brun, Monthly Notices of the Royal Astronomical Society465, 2936–2965 (2016)

work page 2016
[45]

Springel, R

V. Springel, R. Pakmor, A. Pillepich, R. Weinberger, D. Nelson, L. Hernquist, M. Vogelsberger, S. Genel, P. Torrey, F. Marinacci, and J. Naiman, Monthly Notices of the Royal Astronomical Society475, 676–698 (2017)

work page 2017
[46]

Dav´ e, D

R. Dav´ e, D. Angl´ es-Alc´ azar, D. Narayanan, Q. Li, M. H. Rafieferantsoa, and S. Appleby, Monthly Notices of the Royal Astronomical Society486, 2827–2849 (2019). – 19 –

work page 2019
[47]

Villaescusa-Navarro, D

F. Villaescusa-Navarro, D. Angl´ es-Alc´ azar, S. Genel, D. N. Spergel, R. S. Somerville, R. Dave, A. Pillepich, L. Hernquist, D. Nelson, P. Torrey, D. Narayanan, Y. Li, O. Philcox, V. La Torre, A. Maria Delgado, S. Ho, S. Hassan, B. Burkhart, D. Wadekar, N. Battaglia, G. Contardo, and G. L. Bryan, The Astrophysical Journal915, 71 (2021)

work page 2021
[48]

S. Bird, Y. Ni, T. Di Matteo, R. Croft, Y. Feng, and N. Chen, Monthly Notices of the Royal Astronomical Society512, 3703–3716 (2022)

work page 2022
[49]

Schaye, R

J. Schaye, R. Kugel, M. Schaller, J. C. Helly, J. Braspenning, W. Elbers, I. G. McCarthy, M. P. van Daalen, B. Vandenbroucke, C. S. Frenk, J. Kwan, J. Salcido, Y. M. Bah´ e, J. Borrow, E. Chaikin, O. Hahn, F. Huˇ sko, A. Jenkins, C. G. Lacey, and F. S. J. Nobels, Monthly Notices of the Royal Astronomical Society526, 4978–5020 (2023)

work page 2023
[50]

Eifler, E

T. Eifler, E. Krause, S. Dodelson, A. R. Zentner, A. P. Hearin, and N. Y. Gnedin, Monthly Notices of the Royal Astronomical Society454, 2451 (2015), https://academic.oup.com/mnras/article-pdf/454/3/2451/4025072/stv2000.pdf

work page 2015
[51]

Schneider, R

A. Schneider, R. Teyssier, J. Stadel, N. E. Chisari, A. M. L. Brun, A. Amara, and A. Refregier, Journal of Cosmology and Astroparticle Physics2019, 020 (2019)

work page 2019
[52]

Schneider, N

A. Schneider, N. Stoira, A. Refregier, A. J. Weiss, M. Knabenhans, J. Stadel, and R. Teyssier, Journal of Cosmology and Astroparticle Physics2020, 019 (2020)

work page 2020
[53]

Schneider, A

A. Schneider, A. Refregier, S. Grandis, D. Eckert, N. Stoira, T. Kacprzak, M. Knabenhans, J. Stadel, and R. Teyssier, Journal of Cosmology and Astroparticle Physics2020, 020 (2020)

work page 2020
[54]

Constraining baryonic feedback and cosmology from des y3 and planck pr4 6×2pt data. i.λcdm models,

J. Xu, T. Eifler, E. Krause, V. Miranda, J. Salcido, and I. McCarthy, “Constraining baryonic feedback and cosmology from des y3 and planck pr4 6×2pt data. i.λcdm models,” (2026), arXiv:2510.25596 [astro-ph.CO]

work page arXiv 2026
[55]

Lehman, S

K. Lehman, S. Krippendorf, J. Weller, and K. Dolag, Journal of Cosmology and Astroparticle Physics2025, 032 (2025), arXiv:2411.08957 [astro-ph.CO]

work page arXiv 2025
[56]

Bigwood, A

L. Bigwood, A. Amon,et al., Monthly Notices of the Royal Astronomical Society534, 655 (2024), https://academic.oup.com/mnras/article-pdf/534/1/655/59261644/stae2100.pdf

work page 2024
[57]

Bigwood, M

L. Bigwood, M. A. Bourne, V. Irˇ siˇ c, A. Amon, and D. Sijacki, Monthly Notices of the Royal Astronomical Society (2025), 10.1093/mnras/staf1435

work page doi:10.1093/mnras/staf1435 2025
[58]

The kinetic sunyaev zeldovich effect as a benchmark for agn feedback models in hydrodynamical simulations: insights from desi + act,

L. Bigwood, M. Yamamoto, J. Siegel, A. Amon, I. G. McCarthy, R. Dave, J. Salcido, M. Schaller, J. Schaye, and T. Yang, “The kinetic sunyaev zeldovich effect as a benchmark for agn feedback models in hydrodynamical simulations: insights from desi + act,” (2025), arXiv:2510.15822 [astro-ph.CO]

work page arXiv 2025
[59]

Theis, S

A. Theis, S. Hagstotz, R. Reischke, and J. Weller, (2024), arXiv:2403.08611 [astro-ph.CO]

work page arXiv 2024
[60]

Reischke, D

R. Reischke, D. Neumann, K. A. Bertmann, S. Hagstotz, and H. Hildebrandt, (2023), arXiv:2309.09766 [astro-ph.CO]

work page arXiv 2023
[61]

Reischke and S

R. Reischke and S. Hagstotz, (2025), arXiv:2507.17742 [astro-ph.CO]

work page arXiv 2025
[62]

Probing baryonic feedback with fast radio bursts: joint analyses with cosmic shear and galaxy clustering

A. Wayland, D. Alonso, and R. Reischke, “Probing baryonic feedback with fast radio bursts: joint analyses with cosmic shear and galaxy clustering,” (2026), arXiv:2602.12174 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2026
[63]

S. K. Giri and A. Schneider, Journal of Cosmology and Astroparticle Physics2021, 046 (2021)

work page 2021
[64]

A. J. Mead, C. Heymans, L. Lombriser, J. A. Peacock, O. I. Steele, and H. A. Winther, Monthly Notices of the Royal Astronomical Society459, 1468–1488 (2016)

work page 2016
[65]

M. A. Mitchell, C. Arnold, J. hua He, and B. Li, Monthly Notices of the Royal Astronomical Society487, 1410 (2019). – 20 –

work page 2019
[66]

X. Fang, T. Eifler, E. Schaan, H.-J. Huang, E. Krause, and S. Ferraro, Monthly Notices of the Royal Astronomical Society509, 5721 (2021), https://academic.oup.com/mnras/article-pdf/509/4/5721/41759015/stab3410.pdf

work page 2021
[67]

P. L. Taylor, F. Bernardeau, and T. D. Kitching, Physical Review D98(2018), 10.1103/physrevd.98.083514

work page doi:10.1103/physrevd.98.083514 2018
[68]

P. L. Taylor, F. Bernardeau, and E. Huff, Physical Review D103(2021), 10.1103/physrevd.103.043531

work page doi:10.1103/physrevd.103.043531 2021
[69]

Vazsonyi, P

L. Vazsonyi, P. L. Taylor, G. Valogiannis, N. S. Ramachandra, A. Fert´ e, and J. Rhodes, Physical Review D104, 083527 (2021), arXiv:2107.10277 [astro-ph.CO]

work page arXiv 2021
[70]

P. L. Tayloret al., The Open Journal of Astrophysics4, 6 (2021), arXiv:2012.04672 [astro-ph.CO]

work page arXiv 2021
[71]

Bernardeau, T

F. Bernardeau, T. Nishimichi, and A. Taruya, Monthly Notices of the Royal Astronomical Society445, 1526–1537 (2014)

work page 2014
[72]

Barthelemy, F

A. Barthelemy, F. Bernardeau, S. Codis, and C. Uhlemann, Physical Review D105(2022), 10.1103/physrevd.105.043537

work page doi:10.1103/physrevd.105.043537 2022
[73]

Robust cosmic shear with small-scale nulling,

G. Piccirilli, M. Zennaro, C. Garc´ ıa-Garc´ ıa, and D. Alonso, “Robust cosmic shear with small-scale nulling,” (2025), arXiv:2502.17339 [astro-ph.CO]

work page arXiv 2025
[74]

super-screened

B. Bose, M. Cataneo, T. Tr¨ oster, Q. Xia, C. Heymans, and L. Lombriser, arXiv e-prints , arXiv:2005.12184 (2020), arXiv:2005.12184 [astro-ph.CO] . AReACTemulator The halo model reaction formalism [18, 20, 74] is based on a modified version of the halo model, and has been successfully used to accurately predict the matter power spectrum in a variety of ΛC...

work page arXiv 2005