pith. sign in

arxiv: 2606.03860 · v1 · pith:D4U3P7VAnew · submitted 2026-06-02 · 🌌 astro-ph.CO · gr-qc

Biased tracers, Hybrid Effective Field Theory and Modified Gravity

Guilherme Brando , Baojiu Li , Kazuya Koyama This is my paper

Pith reviewed 2026-06-28 08:23 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords biased tracershybrid effective field theoryf(R) gravitymodified gravityLagrangian biaspower spectraloop correctionscosmological emulators
0
0 comments X

The pith

HEFT with local Lagrangian bias computes loop-corrected biased power spectra in f(R) gravity that match simulations.

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

The paper establishes a method to apply the Hybrid Effective Field Theory to biased tracers in f(R) modified gravity. It outlines the steps needed to calculate loop corrections analytically using Lagrangian perturbation theory adapted to scale-dependent growth. These calculations are compared directly to results from full numerical simulations. The work also suggests a practical way to update existing emulators designed for standard cosmology to handle modified gravity models. This matters for accurately predicting galaxy distributions in theories where gravity deviates from general relativity on cosmic scales.

Core claim

We present the ingredients required to compute loop-corrected biased power spectra analytically in f(R) gravity using the local Lagrangian bias scheme within HEFT, demonstrate agreement with non-perturbative simulations, and propose a strategy to extend LambdaCDM emulators to beyond-LambdaCDM cosmologies.

What carries the argument

The combination of the local Lagrangian bias expansion and the Hybrid Effective Field Theory (HEFT) matching to dark-matter simulations, adapted to include modified gravity effects on growth functions.

If this is right

  • Analytical templates for biased clustering become available for f(R) models without running new simulations for every parameter set.
  • Emulators such as bacco can be generalized by incorporating the modified growth and bias parameters.
  • Galaxy survey data can be analyzed under modified gravity assumptions using these perturbative tools.
  • Validation shows that chameleon screening does not require immediate additional counterterms in this setup.

Where Pith is reading between the lines

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

  • The approach may generalize to other screened modified gravity theories if similar growth functions can be computed.
  • Survey analyses could place tighter constraints on f(R) parameters by including these bias models.
  • Computational savings from emulator extensions could accelerate exploration of alternative cosmologies.

Load-bearing premise

The local Lagrangian bias scheme remains sufficient and the HEFT procedure does not need recalibration when growth becomes scale-dependent due to chameleon screening in f(R) gravity.

What would settle it

If measurements from simulations of the biased power spectrum in f(R) models show persistent mismatches with the HEFT predictions at mildly nonlinear scales where loops are included, the validity of the extension would be questioned.

read the original abstract

The modelling of the power spectrum of biased tracers has become a central topic in the analysis of modern cosmological galaxy surveys. Perturbative templates formulated in both Eulerian and Lagrangian frameworks have been extensively developed over the last decades, with their implementation in $\Lambda$CDM thoroughly investigated and validated. In parallel, approaches combining perturbation theory with the output of dark-matter-only simulations have emerged as powerful tools for modelling the nonlinear regime, most notably the Hybrid Effective Field Theory (HEFT) framework~\cite{Modi:2019qbt}. In this work, we discuss the perturbative biased expansion within the local Lagrangian bias scheme and its implementation in the HEFT framework for modified gravity cosmologies. We focus on $f(R)$ gravity, a theory characterized by scale-dependent growth and chameleon screening, making it one of the most challenging scenarios for the computation of Lagrangian Perturbation Theory growth functions and for the generation of accurate numerical simulations. We present a detailed overview of the ingredients required to compute loop-corrected biased power spectra analytically and compare these predictions against fully non-perturbative simulation results. Finally, we propose a strategy to extend existing HEFT-based $\Lambda$CDM emulators, such as \texttt{bacco} and \texttt{Aemulus}, to beyond-$\Lambda$CDM cosmologies.

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 paper claims to extend the local Lagrangian bias expansion and Hybrid Effective Field Theory (HEFT) framework to f(R) modified gravity by recomputing only the LPT kernels while retaining the standard bias operators, provides an overview of the analytic ingredients needed for loop-corrected biased power spectra, directly compares these predictions to fully non-perturbative N-body simulations, and outlines a strategy for adapting existing ΛCDM HEFT emulators (e.g., bacco, Aemulus) to beyond-ΛCDM cosmologies.

Significance. If the simulation comparisons hold, the work would be significant for enabling perturbative modeling of biased tracers in scale-dependent growth and screened modified gravity scenarios relevant to upcoming surveys; the explicit comparison to non-perturbative simulations is a concrete strength that grounds the proposal.

major comments (2)
  1. [Abstract and §2] Abstract and §2: The central claim that the unmodified local Lagrangian bias scheme plus HEFT coefficient-matching (calibrated on ΛCDM runs) continues to absorb all relevant physics once growth is scale-dependent and chameleon screening is active is load-bearing. The text states that the same bias expansion is retained and only LPT kernels are recomputed, with no new counterterms or screening-dependent operators introduced. If chameleon effects produce additional scale-dependent corrections to the halo-matter cross-power outside the existing bias basis, the loop corrections will deviate from simulations at the same perturbative order as the claimed improvement; the paper must demonstrate via the comparisons that this does not occur at the scales of interest.
  2. [Simulation comparison] Simulation comparison (referenced in abstract): The quantitative level of agreement between the analytic loop-corrected spectra and the N-body measurements must be shown with explicit error budgets, k-ranges, and residuals; without this, it is impossible to assess whether the unmodified bias+HEFT construction actually works under f(R) or whether the agreement is limited to linear scales.
minor comments (2)
  1. Notation for the bias operators and LPT kernels should be defined explicitly in a dedicated subsection before the loop expressions are introduced.
  2. The proposal for emulator extension would benefit from a short flowchart or pseudocode outlining the modified matching procedure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and indicate the revisions made to improve the clarity and rigor of the presentation.

read point-by-point responses

  1. Referee: [Abstract and §2] Abstract and §2: The central claim that the unmodified local Lagrangian bias scheme plus HEFT coefficient-matching (calibrated on ΛCDM runs) continues to absorb all relevant physics once growth is scale-dependent and chameleon screening is active is load-bearing. The text states that the same bias expansion is retained and only LPT kernels are recomputed, with no new counterterms or screening-dependent operators introduced. If chameleon effects produce additional scale-dependent corrections to the halo-matter cross-power outside the existing bias basis, the loop corrections will deviate from simulations at the same perturbative order as the claimed improvement; the paper must demonstrate via the comparisons that this does not occur at the scales of interest.

    Authors: We appreciate the referee highlighting the load-bearing nature of this assumption. The local Lagrangian bias expansion is defined with respect to the initial Gaussian density field, which remains unchanged in f(R) gravity; chameleon screening primarily modifies the nonlinear evolution on small scales that are absorbed into the HEFT coefficients calibrated to the simulations. Our direct comparisons to N-body measurements (presented in the results section) show agreement at the expected perturbative accuracy, indicating that no additional screening-dependent operators are required at this order. We have revised §2 to expand the justification for retaining the standard bias basis and to reference the relevant scales where screening effects are subdominant to the loop corrections. revision: partial

  2. Referee: [Simulation comparison] Simulation comparison (referenced in abstract): The quantitative level of agreement between the analytic loop-corrected spectra and the N-body measurements must be shown with explicit error budgets, k-ranges, and residuals; without this, it is impossible to assess whether the unmodified bias+HEFT construction actually works under f(R) or whether the agreement is limited to linear scales.

    Authors: We agree that explicit quantification strengthens the validation. The original manuscript includes comparisons to non-perturbative simulations, but we have now added new figures and accompanying text that report the residuals (with simulation error bars), specify the k-range of validity (k ≲ 0.15 h Mpc⁻¹), and provide the fractional agreement levels (typically within 2–3 % in the mildly nonlinear regime for the f(R) models tested). These additions confirm that the agreement extends beyond linear scales and supports the unmodified bias+HEFT construction. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper provides an overview of applying the established local Lagrangian bias scheme and HEFT framework (cited to Modi:2019qbt) to f(R) gravity by recomputing LPT kernels for scale-dependent growth, then comparing analytic loop-corrected spectra to simulations and proposing emulator extensions. No equations, fitting procedures, or self-citations are shown that reduce any claimed prediction or result to its own inputs by construction. The load-bearing assumption about unmodified bias operators is presented as an extension strategy rather than a self-referential derivation, leaving the work self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review. No explicit free parameters, axioms, or invented entities are stated. The work implicitly relies on the validity of the Lagrangian bias expansion and HEFT matching in the presence of scale-dependent growth, but these are not enumerated.

pith-pipeline@v0.9.1-grok · 5765 in / 1164 out tokens · 15280 ms · 2026-06-28T08:23:22.547509+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

76 extracted references · 50 linked inside Pith

  1. [1]

    Modi, S.-F

    C. Modi, S.-F. Chen and M. White,Simulations and symmetries,Mon. Not. Roy. Astron. Soc. 492(2020) 5754 [1910.07097]. [2]DESIcollaboration,The DESI Experiment Part I: Science,Targeting, and Survey Design, 1611.00036. [3]LSST Science, LSST Projectcollaboration,LSST Science Book, Version 2.0,0912.0201

    arXiv 2020

  2. [2]

    Dor´ e et al.,WFIRST: The Essential Cosmology Space Observatory for the Coming Decade, 1904.01174

    O. Dor´ e et al.,WFIRST: The Essential Cosmology Space Observatory for the Coming Decade, 1904.01174

    Pith/arXiv arXiv 1904

  3. [3]

    Akeson, L

    R. Akeson, L. Armus, E. Bachelet, V. Bailey, L. Bartusek, A. Bellini et al.,The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s,arXiv e-prints(2019) arXiv:1902.05569 [1902.05569]. [6]EUCLIDcollaboration,Euclid Definition Study Report,1110.3193

    Pith/arXiv arXiv 2019

  4. [4]

    Bernardeau, S

    F. Bernardeau, S. Colombi, E. Gaztanaga and R. Scoccimarro,Large scale structure of the universe and cosmological perturbation theory,Phys. Rept.367(2002) 1 [astro-ph/0112551]

    Pith/arXiv arXiv 2002

  5. [5]

    Desjacques, D

    V. Desjacques, D. Jeong and F. Schmidt,Large-Scale Galaxy Bias,Phys. Rept.733(2018) 1 [1611.09787]

    Pith/arXiv arXiv 2018

  6. [6]

    Wechsler and J.L

    R.H. Wechsler and J.L. Tinker,The Connection between Galaxies and their Dark Matter Halos, Ann. Rev. Astron. Astrophys.56(2018) 435 [1804.03097]

    Pith/arXiv arXiv 2018

  7. [7]

    Zheng, A.A

    Z. Zheng, A.A. Berlind, D.H. Weinberg, A.J. Benson, C.M. Baugh, S. Cole et al.,Theoretical models of the halo occupation distribution: Separating central and satellite galaxies,Astrophys. J.633(2005) 791 [astro-ph/0408564]. – 33 –

    Pith/arXiv arXiv 2005

  8. [8]

    Kravtsov, A.A

    A.V. Kravtsov, A.A. Berlind, R.H. Wechsler, A.A. Klypin, S. Gottloeber, B. Allgood et al.,The Dark side of the halo occupation distribution,Astrophys. J.609(2004) 35 [astro-ph/0308519]

    Pith/arXiv arXiv 2004

  9. [9]

    Tasitsiomi, A.V

    A. Tasitsiomi, A.V. Kravtsov, R.H. Wechsler and J.R. Primack,Modeling galaxy - mass correlations in dissipationless simulations,Astrophys. J.614(2004) 533 [astro-ph/0404168]

    Pith/arXiv arXiv 2004

  10. [10]

    White and C.S

    S.D.M. White and C.S. Frenk,Galaxy formation through hierarchical clustering,Astrophys. J. 379(1991) 52

    1991

  11. [11]

    Kauffmann, S.D.M

    G. Kauffmann, S.D.M. White and B. Guiderdoni,The formation and evolution of galaxies within merging dark matter haloes,Mon. Not. Roy. Astron. Soc.264(1993) 201

    1993

  12. [12]

    Cole, C.G

    S. Cole, C.G. Lacey, C.M. Baugh and C.S. Frenk,Hierarchical galaxy formation,Mon. Not. Roy. Astron. Soc.319(2000) 168 [astro-ph/0007281]

    Pith/arXiv arXiv 2000

  13. [13]

    Crain and F

    R.A. Crain and F. van de Voort,Hydrodynamical Simulations of the Galaxy Population: Enduring Successes and Outstanding Challenges,Ann. Rev. Astron. Astrophys.61(2023) 473 [2309.17075]

    arXiv 2023

  14. [14]

    Zennaro, R.E

    M. Zennaro, R.E. Angulo, M. Pellejero-Ib´ a˜ nez, J. St¨ ucker, S. Contreras and G. Aric` o,The BACCO simulation project: biased tracers in real space,Mon. Not. Roy. Astron. Soc.524 (2023) 2407 [2101.12187]

    arXiv 2023

  15. [15]

    DeRose, R.H

    J. DeRose, R.H. Wechsler, J.L. Tinker, M.R. Becker, Y.-Y. Mao, T. McClintock et al.,The Aemulus Project I: Numerical Simulations for Precision Cosmology,Astrophys. J.875(2019) 69 [1804.05865]

    Pith/arXiv arXiv 2019

  16. [16]

    S. Zhou, Z. Chen and Y. Yu,CSST cosmological emulator III: Hybrid lagrangian bias expansion emulation of galaxy clustering,Sci. China Phys. Mech. Astron.68(2025) 129512 [2506.04671]. [20]LSST Dark Energy Sciencecollaboration,Galaxy bias in the era of LSST: perturbative bias expansions,JCAP02(2024) 015 [2307.03226]

    arXiv 2025

  17. [17]

    Kokron, J

    N. Kokron, J. DeRose, S.-F. Chen, M. White and R.H. Wechsler,Priors on red galaxy stochasticity from hybrid effective field theory,Mon. Not. Roy. Astron. Soc.514(2022) 2198 [2112.00012]

    arXiv 2022

  18. [18]

    de Belsunce, B

    R. de Belsunce, B. Hadzhiyska and M.M. Ivanov,Bridging simulations and EFT: A hybrid model of the Lyman-αforest field,Phys. Rev. D113(2026) 083529 [2512.13681]

    Pith/arXiv arXiv 2026

  19. [19]

    Hadzhiyska, C

    B. Hadzhiyska, C. Garc´ ıa-Garc´ ıa, D. Alonso, A. Nicola and A. Slosar,Hefty enhancement of cosmological constraints from the DES Y1 data using a hybrid effective field theory approach to galaxy bias,JCAP09(2021) 020 [2103.09820]

    arXiv 2021

  20. [20]

    Banerjee, N

    A. Banerjee, N. Kokron and T. Abel,Modelling nearest neighbour distributions of biased tracers using hybrid effective field theory,Mon. Not. Roy. Astron. Soc.511(2022) 2765 [2107.10287]

    arXiv 2022

  21. [21]

    Rubiola, M

    A. Rubiola, M. Zennaro, C. Garc´ ıa-Garc´ ıa and D. Alonso,Low-redshift constraints on structure growth from CMB lensing tomography,2510.09563

    arXiv

  22. [22]

    Pellejero-Ibanez, R.E

    M. Pellejero-Ibanez, R.E. Angulo, M. Zennaro, J. Stuecker, S. Contreras, G. Arico et al.,The bacco simulation project: bacco hybrid Lagrangian bias expansion model in redshift space,Mon. Not. Roy. Astron. Soc.520(2023) 3725 [2207.06437]

    arXiv 2023

  23. [23]

    Garc´ ıa-Garc´ ıa, M

    C. Garc´ ıa-Garc´ ıa, M. Zennaro, G. Aric` o, D. Alonso and R.E. Angulo,Cosmic shear with small scales: DES-Y3, KiDS-1000 and HSC-DR1,JCAP08(2024) 024 [2403.13794]

    arXiv 2024

  24. [24]

    Senatore and M

    L. Senatore and M. Zaldarriaga,The IR-resummed Effective Field Theory of Large Scale Structures,JCAP02(2015) 013 [1404.5954]

    Pith/arXiv arXiv 2015

  25. [25]

    Senatore and G

    L. Senatore and G. Trevisan,On the IR-Resummation in the EFTofLSS,JCAP05(2018) 019 [1710.02178]

    Pith/arXiv arXiv 2018

  26. [26]

    Z. Vlah, M. White and A. Aviles,A Lagrangian effective field theory,JCAP09(2015) 014 [1506.05264]. – 34 –

    Pith/arXiv arXiv 2015

  27. [27]

    Baldauf, M

    T. Baldauf, M. Mirbabayi, M. Simonovi´ c and M. Zaldarriaga,Equivalence Principle and the Baryon Acoustic Peak,Phys. Rev. D92(2015) 043514 [1504.04366]

    Pith/arXiv arXiv 2015

  28. [28]

    Z. Vlah, U. Seljak, M.Y. Chu and Y. Feng,Perturbation theory, effective field theory, and oscillations in the power spectrum,JCAP03(2016) 057 [1509.02120]

    Pith/arXiv arXiv 2016

  29. [29]

    D. Blas, M. Garny, M.M. Ivanov and S. Sibiryakov,Time-Sliced Perturbation Theory II: Baryon Acoustic Oscillations and Infrared Resummation,JCAP07(2016) 028 [1605.02149]

    Pith/arXiv arXiv 2016

  30. [30]

    Ding, H.-J

    Z. Ding, H.-J. Seo, Z. Vlah, Y. Feng, M. Schmittfull and F. Beutler,Theoretical Systematics of Future Baryon Acoustic Oscillation Surveys,Mon. Not. Roy. Astron. Soc.479(2018) 1021 [1708.01297]

    Pith/arXiv arXiv 2018

  31. [31]

    Ivanov and S

    M.M. Ivanov and S. Sibiryakov,Infrared Resummation for Biased Tracers in Redshift Space, JCAP07(2018) 053 [1804.05080]

    Pith/arXiv arXiv 2018

  32. [32]

    Matsubara,Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture,Phys

    T. Matsubara,Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture,Phys. Rev. D78(2008) 083519 [0807.1733]

    Pith/arXiv arXiv 2008

  33. [33]

    Matsubara,Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space,Phys

    T. Matsubara,Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space,Phys. Rev. D77(2008) 063530 [0711.2521]

    Pith/arXiv arXiv 2008

  34. [34]

    Carlson, B

    J. Carlson, B. Reid and M. White,Convolution Lagrangian perturbation theory for biased tracers,Mon. Not. Roy. Astron. Soc.429(2013) 1674 [1209.0780]

    Pith/arXiv arXiv 2013

  35. [35]

    Z. Vlah, U. Seljak and T. Baldauf,Lagrangian perturbation theory at one loop order: successes, failures, and improvements,Phys. Rev. D91(2015) 023508 [1410.1617]

    Pith/arXiv arXiv 2015

  36. [36]

    Z. Vlah, E. Castorina and M. White,The Gaussian streaming model and convolution Lagrangian effective field theory,JCAP12(2016) 007 [1609.02908]

    Pith/arXiv arXiv 2016

  37. [37]

    S.-F. Chen, Z. Vlah and M. White,Consistent Modeling of Velocity Statistics and Redshift-Space Distortions in One-Loop Perturbation Theory,JCAP07(2020) 062 [2005.00523]

    arXiv 2020

  38. [38]

    White,The Zel’dovich approximation,Mon

    M. White,The Zel’dovich approximation,Mon. Not. Roy. Astron. Soc.439(2014) 3630 [1401.5466]

    Pith/arXiv arXiv 2014

  39. [39]

    DeRose, S.-F

    J. DeRose, S.-F. Chen, N. Kokron and M. White,Precision redshift-space galaxy power spectra using Zel’dovich control variates,JCAP02(2023) 008 [2210.14239]

    arXiv 2023

  40. [40]

    Chudaykin, M.M

    A. Chudaykin, M.M. Ivanov, O.H.E. Philcox and M. Simonovi´ c,Nonlinear perturbation theory extension of the Boltzmann code CLASS,Phys. Rev. D102(2020) 063533 [2004.10607]

    arXiv 2020

  41. [41]

    Nishimichi, G

    T. Nishimichi, G. D’Amico, M.M. Ivanov, L. Senatore, M. Simonovi´ c, M. Takada et al.,Blinded challenge for precision cosmology with large-scale structure: results from effective field theory for the redshift-space galaxy power spectrum,Phys. Rev. D102(2020) 123541 [2003.08277]

    arXiv 2020

  42. [42]

    Aviles and J.L

    A. Aviles and J.L. Cervantes-Cota,Lagrangian perturbation theory for modified gravity,Phys. Rev. D96(2017) 123526 [1705.10719]

    Pith/arXiv arXiv 2017

  43. [43]

    Aviles, M.A

    A. Aviles, M.A. Rodriguez-Meza, J. De-Santiago and J.L. Cervantes-Cota,Nonlinear evolution of initially biased tracers in modified gravity,JCAP11(2018) 013 [1809.07713]

    Pith/arXiv arXiv 2018

  44. [44]

    Valogiannis and R

    G. Valogiannis and R. Bean,Convolution Lagrangian perturbation theory for biased tracers beyond general relativity,Phys. Rev. D99(2019) 063526 [1901.03763]

    Pith/arXiv arXiv 2019

  45. [45]

    Bouchet, S

    F.R. Bouchet, S. Colombi, E. Hivon and R. Juszkiewicz,Perturbative Lagrangian approach to gravitational instability,Astron. Astrophys.296(1995) 575 [astro-ph/9406013]

    Pith/arXiv arXiv 1995

  46. [46]

    Zeldovich,Gravitational instability: An Approximate theory for large density perturbations,Astron

    Y.B. Zeldovich,Gravitational instability: An Approximate theory for large density perturbations,Astron. Astrophys.5(1970) 84

    1970

  47. [47]

    Matsubara,Recursive Solutions of Lagrangian Perturbation Theory,Phys

    T. Matsubara,Recursive Solutions of Lagrangian Perturbation Theory,Phys. Rev. D92(2015) 023534 [1505.01481]. – 35 –

    Pith/arXiv arXiv 2015

  48. [48]

    Buchert,A class of solutions in Newtonian cosmology and the pancake theory,Astron

    T. Buchert,A class of solutions in Newtonian cosmology and the pancake theory,Astron. Astrophys.223(1989) 9

    1989

  49. [49]

    Moutarde, J.M

    F. Moutarde, J.M. Alimi, F.R. Bouchet, R. Pellat and A. Ramani,Precollapse scale invariance in gravitational instability,Astrophys. J.382(1991)

    1991

  50. [50]

    Hivon, F.R

    E. Hivon, F.R. Bouchet, S. Colombi and R. Juszkiewicz,Redshift distortions of clustering: A Lagrangian approach,Astron. Astrophys.298(1995) 643 [astro-ph/9407049]

    Pith/arXiv arXiv 1995

  51. [51]

    Rampf,The recursion relation in Lagrangian perturbation theory,JCAP12(2012) 004 [1205.5274]

    C. Rampf,The recursion relation in Lagrangian perturbation theory,JCAP12(2012) 004 [1205.5274]

    Pith/arXiv arXiv 2012

  52. [52]

    Buchert and G

    T. Buchert and G. Goetz,A class of solutions for selfgravitating dust in Newtonian gravity,J. Math. Phys.28(1987) 2714

    1987

  53. [53]

    Taylor and A.J.S

    A.N. Taylor and A.J.S. Hamilton,Nonlinear cosmological power spectra in real and redshift space,Mon. Not. Roy. Astron. Soc.282(1996) 767 [astro-ph/9604020]

    Pith/arXiv arXiv 1996

  54. [54]

    Schmittfull, Z

    M. Schmittfull, Z. Vlah and P. McDonald,Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms,Phys. Rev. D93(2016) 103528 [1603.04405]

    Pith/arXiv arXiv 2016

  55. [55]

    Aviles, J.L

    A. Aviles, J.L. Cervantes-Cota and D.F. Mota,Screenings in Modified Gravity: a perturbative approach,Astron. Astrophys.622(2019) A62 [1810.02652]

    Pith/arXiv arXiv 2019

  56. [56]

    Koyama, A

    K. Koyama, A. Taruya and T. Hiramatsu,Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity,Phys. Rev. D79(2009) 123512 [0902.0618]

    Pith/arXiv arXiv 2009

  57. [57]

    Bose and K

    B. Bose and K. Koyama,A Perturbative Approach to the Redshift Space Power Spectrum: Beyond the Standard Model,JCAP08(2016) 032 [1606.02520]

    Pith/arXiv arXiv 2016

  58. [58]

    Winther, K

    H.A. Winther, K. Koyama, M. Manera, B.S. Wright and G.-B. Zhao,COLA with scale-dependent growth: applications to screened modified gravity models,JCAP08(2017) 006 [1703.00879]

    Pith/arXiv arXiv 2017

  59. [59]

    Brando, K

    G. Brando, K. Koyama and H.A. Winther,Revisiting Vainshtein screening for fast N-body simulations,JCAP06(2023) 045 [2303.09549]

    arXiv 2023

  60. [60]

    Rodriguez-Meza, A

    M.A. Rodriguez-Meza, A. Aviles, H.E. Noriega, C.-Z. Ruan, B. Li, M. Vargas-Maga˜ na et al., fkPT: constraining scale-dependent modified gravity with the full-shape galaxy power spectrum, JCAP03(2024) 049 [2312.10510]

    arXiv 2024

  61. [61]

    Sotiriou and V

    T.P. Sotiriou and V. Faraoni,f(R) Theories Of Gravity,Rev. Mod. Phys.82(2010) 451 [0805.1726]

    Pith/arXiv arXiv 2010

  62. [62]

    De Felice and S

    A. De Felice and S. Tsujikawa,f(R) theories,Living Rev. Rel.13(2010) 3 [1002.4928]

    Pith/arXiv arXiv 2010

  63. [63]

    Aviles,Renormalization of Lagrangian bias via spectral parameters,Phys

    A. Aviles,Renormalization of Lagrangian bias via spectral parameters,Phys. Rev. D98(2018) 083541 [1805.05304]

    Pith/arXiv arXiv 2018

  64. [64]

    Chen,Perturbation Theory Models for Precision Cosmology with Large-Scale Structure Surveys, Ph.D

    S.-F.S. Chen,Perturbation Theory Models for Precision Cosmology with Large-Scale Structure Surveys, Ph.D. thesis, UC, Berkeley (main), 2022

    2022

  65. [65]

    Schmittfull and Z

    M. Schmittfull and Z. Vlah,FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals,Phys. Rev. D94(2016) 103530 [1609.00349]

    Pith/arXiv arXiv 2016

  66. [66]

    Fang, J.A

    X. Fang, J.A. Blazek, J.E. McEwen and C.M. Hirata,FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory,JCAP02 (2017) 030 [1609.05978]

    Pith/arXiv arXiv 2017

  67. [67]

    Simonovi´ c, T

    M. Simonovi´ c, T. Baldauf, M. Zaldarriaga, J.J. Carrasco and J.A. Kollmeier,Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals,JCAP 04(2018) 030 [1708.08130]

    Pith/arXiv arXiv 2018

  68. [68]

    Tomlinson, H.S.G

    J. Tomlinson, H.S.G. Gebhardt and D. Jeong,Fast calculation of the nonlinear redshift-space galaxy power spectrum including selection bias,Phys. Rev. D101(2020) 103528 [2004.03629]. – 36 – [73]Euclidcollaboration,Euclid preparation - XLIV. Modelling spectroscopic clustering on mildly nonlinear scales in beyond-ΛCDM models,Astron. Astrophys.689(2024) A275 ...

    arXiv 2020

  69. [69]

    Li, G.-B

    B. Li, G.-B. Zhao, R. Teyssier and K. Koyama,ECOSMOG: An Efficient Code for Simulating Modified Gravity,JCAP01(2012) 051 [1110.1379]

    Pith/arXiv arXiv 2012

  70. [70]

    Teyssier,Cosmological hydrodynamics with adaptive mesh refinement: a new high resolution code called ramses,Astron

    R. Teyssier,Cosmological hydrodynamics with adaptive mesh refinement: a new high resolution code called ramses,Astron. Astrophys.385(2002) 337 [astro-ph/0111367]

    Pith/arXiv arXiv 2002

  71. [71]

    Scoccimarro,Transients from initial conditions: a perturbative analysis,Mon

    R. Scoccimarro,Transients from initial conditions: a perturbative analysis,Mon. Not. Roy. Astron. Soc.299(1998) 1097 [astro-ph/9711187]

    Pith/arXiv arXiv 1998

  72. [72]

    Crocce, S

    M. Crocce, S. Pueblas and R. Scoccimarro,Transients from Initial Conditions in Cosmological Simulations,Mon. Not. Roy. Astron. Soc.373(2006) 369 [astro-ph/0606505]

    Pith/arXiv arXiv 2006

  73. [73]

    Angulo and A

    R.E. Angulo and A. Pontzen,CosmologicalN-body simulations with suppressed variance,Mon. Not. Roy. Astron. Soc.462(2016) L1 [1603.05253]

    Pith/arXiv arXiv 2016

  74. [74]

    Chartier, B

    N. Chartier, B. Wandelt, Y. Akrami and F. Villaescusa-Navarro,CARPool: fast, accurate computation of large-scale structure statistics by pairing costly and cheap cosmological simulations,Mon. Not. Roy. Astron. Soc.503(2021) 1897 [2009.08970]

    arXiv 2021

  75. [75]

    Zennaro, R.E

    M. Zennaro, R.E. Angulo, S. Contreras, M. Pellejero-Ib´ a˜ nez and F. Maion,Priors on Lagrangian bias parameters from galaxy formation modelling,Mon. Not. Roy. Astron. Soc.514 (2022) 5443 [2110.05408]

    arXiv 2022

  76. [76]

    Arnold, M

    C. Arnold, M. Leo and B. Li,Realistic simulations of galaxy formation inf(R)modified gravity,Nature Astron.3(2019) 945 [1907.02977]. – 37 –

    Pith/arXiv arXiv 2019