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REVIEW 2 major objections 6 minor 55 references

A direct ODE method lets one-loop galaxy clustering predictions keep exact time dependence for Vainshtein-screened modified gravity at only modest extra cost, and BOSS full-shape data visibly tighten the resulting amplitude constraints.

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2026-07-30 16:12 UTC pith:SSBROKPY

load-bearing objection Solid methods paper: faster exact-time one-loop kernels for Vainshtein Horndeski in PyBird, with real N-body checks and tighter c_B–c_M constraints once BOSS FS is in. the 2 major comments →

arxiv 2607.26945 v1 pith:SSBROKPY submitted 2026-07-29 astro-ph.CO

An efficient one-loop EFTofLSS framework for Vainshtein-screened Horndeski gravity

Stan Verhoeve , Dani de Boe , Gen Ye , Alessandra Silvestri This is my paper
classification astro-ph.CO
keywords EFTofLSSHorndeski gravityVainshtein screeningone-loop power spectrumfull-shape analysismodified gravityexact time dependenceBOSS
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Stage-IV surveys will measure galaxy clustering deep into the mildly nonlinear regime, so tests of gravity need accurate one-loop power spectra for theories beyond general relativity. This paper extends an existing EFTofLSS code to quasi-static, Vainshtein-screened luminal Horndeski models (and nDGP) and replaces the usual Green’s-function construction of the time-dependent kernels with a direct forward ODE integration. The new solver is numerically equivalent at the 10^{-6} level, scales independently of the number of redshifts, and keeps the exact time dependence at only a few-percent overhead. One-loop matter spectra match N-body boosts at the sub-percent level for a representative EFTofDE parametrization. Applied to Planck CMB, BOSS full-shape multipoles and DESI BAO, the pipeline shows that full-shape information substantially shrinks the allowed region in the braiding–Planck-mass-run plane; the same machinery also produces ready-to-use multipoles for the cubic Galileon and nDGP. The authors conclude that the Einstein–de Sitter shortcut is no longer required for routine analyses and may even bias posteriors once survey precision rises.

Core claim

A direct ODE integration of the scalar time-dependent coefficients that enter the one-loop perturbation kernels is mathematically equivalent to the Green’s-function convolution, yet cheaper and redshift-independent; once embedded in an EFTofLSS pipeline it yields validated one-loop galaxy multipoles for any quasi-static Vainshtein-screened luminal Horndeski model (or nDGP) and tightens present-day constraints on the EFTofDE amplitudes once BOSS full-shape data are included.

What carries the argument

The factorized ansatz that writes every nth-order density and velocity kernel as a product of purely geometric vertices and a small set of scalar functions of scale factor; those functions obey linear ODEs that are integrated once from deep matter domination, replacing repeated Green’s-function convolutions.

Load-bearing premise

The quasi-static approximation and the assumption that growth remains scale-independent must hold for every mode and redshift that enters the likelihood; if either fails inside the analysis window the kernels and the reported posteriors become invalid.

What would settle it

Re-run the identical one-loop versus N-body boost comparison (or a full MCMC) for a model that violates the sound-speed cut cs ≳ 0.1 or develops clear scale-dependent growth inside k ≲ 0.23 h Mpc^{-1}; a systematic residual larger than the claimed sub-percent agreement would falsify the method’s domain of validity.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Exact time-dependent kernels can be kept by default in future Stage-IV full-shape analyses without a meaningful runtime penalty.
  • Full-shape multipoles, not BAO alone, supply the dominant tightening of braiding and Planck-mass-run amplitudes once CMB priors are fixed.
  • The same modular interface immediately supplies one-loop predictions for any covariant luminal Horndeski theory once its background and α-functions are supplied.
  • Discrepancies between EdS and exact kernels grow with departure from ΛCDM and can reach several σ near the BOSS k_max, so EdS-based posteriors may be biased for strong modified-gravity scenarios.

Where Pith is reading between the lines

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

  • Once the ODE solver is public, the computational barrier to including the bispectrum or two-loop power spectrum for the same class of models drops sharply.
  • Surveys whose effective redshift is lower than BOSS will see a larger EdS–exact mismatch for Ω_DE-proportional models, making the exact treatment more, not less, necessary.
  • The modular α-function interface can be reused as a rapid filter to decide which covariant theories are worth expensive N-body campaigns.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The manuscript extends PyBird to one-loop EFTofLSS analyses of quasi-static, Vainshtein-screened luminal Horndeski models (EFTofDE and covariant) and nDGP. It replaces the Green’s-function construction of the time-dependent kernel coefficients with a direct forward ODE integration, reports O(10^{-6}) numerical agreement with Green’s functions and improved multi-redshift wall time, validates the one-loop matter boost against PySCo-EFT/ECOSMOG-EFT N-body for a representative α_i∝Ω_DE point, and derives Planck+BOSS FS+DESI DR2 BAO constraints on the α_i∝ a^3 and α_i∝Ω_DE amplitudes. Showcase multipoles are given for cubic Galileon and nDGP, and the EdS versus exact-kernel difference is quantified at fixed EFT parameters.

Significance. This is a useful, practical methods contribution for Stage-III/IV full-shape analyses of a well-defined MG class. Strengths that should be credited explicitly are: (i) mathematical equivalence of the ODE and Green’s routes with independent cross-checks at the 10^{-6} level across ΛCDM, wCDM, quintessence, nDGP and cubic Galileon; (ii) a modular API fed by H-EFTCAMB (or any solver supplying α_i and background quantities); (iii) sub-percent agreement of the one-loop matter boost with independent N-body for a representative EFTofDE point; (iv) concrete demonstration that exact time dependence costs only a few percent overhead on a full one-loop multipole evaluation. The published c_B–c_M posteriors and the EdS-versus-exact comparison give the community a ready pipeline rather than a purely formal proposal.

major comments (2)
  1. [Section 4.3, Figure 3] Section 4.3 / Fig. 3 validates only the real-space, unbiased one-loop matter boost R(k)≡P_EFT/P_ΛCDM at z=0 after fitting a single c_ct for k<0.3 h Mpc^{-1}. The likelihood (Sec. 4.5, 5.2) uses redshift-space galaxy monopole and quadrupole with the full bias/counterterm/stochastic set. The manuscript should state more clearly what is and is not tested (matter vs tracers; z=0 vs BOSS effective z; boost vs absolute P(k)), and either add a short discussion of residual theory systematics on the multipoles or flag this as a limitation of the validation, not of the ODE method itself.
  2. [Section 5.4, Figure 7] Section 5.4 shows that at fixed BOSS best-fit EFT parameters the EdS–exact multipole difference can reach ~1σ (fiducial) to ~4σ (extreme c_B, c_M) relative to the BOSS covariance diagonal near k_max. The text then argues this “could plausibly distort the shape of the c_B–c_M posterior” but does not re-run even a limited MCMC with EdS kernels. That leaves the central claim that exact time dependence “may become relevant for future surveys” only partially substantiated. A short EdS-versus-exact posterior comparison on the same chains (or a clear statement that this is deferred and why fixed-parameter σ-levels are still informative) would make the section load-bearing rather than illustrative.
minor comments (6)
  1. [Section 2, Eq. (2.5)] Equation (2.5) and footnote 1: the α_B convention (minus one-half relative to Bellini & Sawicki) is easy to miss when comparing to other EFTofDE papers; consider repeating the factor in the caption of Fig. 5 / Table 2.
  2. [Section 4.4] Section 4.4: the cut c_s ≳ 0.1 is stated but not shown as a function of the sampled (c_B, c_M) posterior; a brief note on how often the cut is active in the chains would help readers assess the QSA domain.
  3. [Section 5.2, Table 2] Table 2 and Fig. 5: report the GR point (c_B=c_M=0) compatibility more quantitatively (e.g. Δχ² or posterior odds) rather than only “consistent within 95% CL”.
  4. [Section 4.2, Figure 2] Figure 2 caption: clarify whether timings include JAX acceleration or pure NumPy/SciPy on one core, for reproducibility against the ~300–400 ms full one-loop figure quoted in the text.
  5. Typos / polish: “andadoptthe”, “Thepaperisstructuredasfollows”, “Wefindthattheinclusion” and similar missing spaces appear in the compiled text; a full proofread pass is needed. Also “α i ∝a 3” spacing in the abstract and Sec. 5 is inconsistent.
  6. [Appendix A] Appendix A: the Green’s-function integral forms are given for documentation, but the ODE right-hand sides actually solved in the code are not written explicitly; adding those ODEs (or a pointer to the public repository routines) would help re-implementers.

Circularity Check

0 steps flagged

No significant circularity: methods reformulation plus external-data constraints

full rationale

The paper’s load-bearing claims are (i) a direct-ODE rewrite of the standard Green’s-function construction for time-dependent SPT kernels, openly presented as mathematically equivalent and cross-checked at O(10^{-6}) against both stock PyBird and an independent Green’s implementation; (ii) sub-percent agreement of the one-loop boost with external N-body runs for α_i∝Ω_DE; and (iii) posterior constraints on c_B, c_M from Planck CMB, BOSS full-shape, and DESI DR2 BAO. None of these reduce by construction to fitted inputs or to a self-citation uniqueness chain. The nonlinear Poisson coefficients μ_Φ, μ_Φ,2, μ_Φ,22 are taken from the external Cusin–Lewandowski–Vernizzi EFTofDE literature; bias/counterterm structure follows standard EFTofLSS; nuisance parameters are marginalized against external clustering data. Self-use of H–EFTCAMB supplies linear spectra as a modular input, not a circular definition of the one-loop kernels or of the reported posteriors. Equivalence of ODE and Green’s methods is a computational identity, not a self-definitional prediction. Score 0 is appropriate.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central claims rest on the standard quasi-static Vainshtein-screened luminal Horndeski effective fluid, the EFTofLSS bias and counterterm expansion, and two common phenomenological time dependences for the α_i. No new physical entities are postulated; free parameters are the usual cosmological, bias, counterterm and α-amplitude coefficients fitted to data.

free parameters (5)
  • c_B, c_M (EFTofDE amplitudes) = posterior means e.g. c_B≈-0.41, c_M≈0.32 (Ω_DE, CMB+FS+BAO)
    Constant coefficients in α_i(a)=c_i a^3 or α_i(a)=c_i Ω_DE(a); sampled with flat priors [-5,5] and constrained by the data.
  • c_K = 0.01 (fixed)
    Kineticity fixed by hand to 0.01 for numerical stability; stated to be irrelevant for the observables.
  • b1, c2, b3 and EFT counter/stochastic terms
    Standard galaxy bias and EFTofLSS nuisance parameters; some analytically marginalized, priors taken from prior PyBird analyses.
  • six ΛCDM cosmological parameters {A_s, n_s, ω_b, ω_c, H_0, τ}
    Sampled with standard flat/Gaussian priors; constrained jointly with MG amplitudes.
  • single counterterm c_ct in N-body comparison
    Fitted to N-body P(k) for k<0.3 h/Mpc when validating the matter boost; all other EFT coefficients set to zero.
axioms (6)
  • domain assumption Quasi-static approximation and non-relativistic limit are valid on the scales and redshifts of the analysis.
    Invoked from Sec. 2 onward; enforced by c_s≳0.1 cut (Sec. 4.4).
  • domain assumption Growth is scale-independent (μ_Φ=μ_Φ(a) only), allowing factorized time-dependent kernels.
    Stated after Eq. (3.1); peculiar to Vainshtein-screened models and required for the ansatz (3.11).
  • domain assumption Luminal GW speed α_T=0 and Vainshtein screening dominate, so μ_Φ,3=0 and the nonlinear Poisson equation truncates as in Eqs. (2.6)–(2.8).
    Sec. 2; follows from GW170817-motivated restriction to luminal Horndeski.
  • domain assumption Standard EFTofLSS bias expansion and counterterms remain valid for this class of MG (bootstrap argument).
    Sec. 3.3 citing D’Amico et al. 2021; reduces seven bias coefficients to four for the one-loop power spectrum.
  • ad hoc to paper Background dark-energy equation of state fixed to w=-1 for the phenomenological runs.
    Sec. 4.4; simplifies the analysis to pure perturbation-sector modifications.
  • standard math Mathematical equivalence of the direct ODE system to the Green’s-function convolution for smooth sources.
    Sec. 3.2; used to justify replacing the original PyBird implementation.

pith-pipeline@v1.2.0-daily-grok45 · 26808 in / 3591 out tokens · 58298 ms · 2026-07-30T16:12:58.312335+00:00 · methodology

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read the original abstract

We present an extension of \texttt{PyBird} for one-loop large-scale structure analyses of modified gravity models. We implement support for quasi-static, Vainshtein-screened luminal Horndeski models (in EFTofDE and covariant formalisms) and nDGP, and replace the Green's function approach with a direct ODE method for computing the exact time-dependent functions entering the perturbation kernels. The new implementation improves computational efficiency while maintaining numerical consistency with the standard approach, and we validate the resulting one-loop matter power spectrum against $N$-body simulations for the $\alpha_i\propto\Omega_{\rm DE}$ parametrization. We apply this framework to constrain the $\alpha_i \propto a^3$ and $\alpha_i \propto \Omega_{\rm DE}$ parametrizations using Planck CMB, BOSS full-shape, and DESI DR2 BAO data, finding that full-shape information significantly tightens the constraints. We further showcase the pipeline for the cubic Galileon and nDGP models, demonstrating its applicability beyond the phenomenological amplitude parametrizations to covariant modified-gravity theories. Finally, we assess the impact of the Einstein--de Sitter approximation and find that exact time dependence can be retained at modest computational cost, which may become relevant for future large-scale structure surveys.

discussion (0)

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