{"id":"41b6c555-85e0-4eb0-954c-63f82b1876e5","arxiv_id":"2607.24940","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.5,"correctness_risk":"low","formal_verification":"none","parameter_count":5,"one_line_summary":"A unified AMR N-body code embeds EFTofDE α-basis models into one master Vainshtein equation and matches legacy ECOSMOG and HiCOLA matter power spectra.","lead":"EFT-RAMSES is a new N-body code that simulates many dark-energy and modified-gravity models through one shared nonlinear equation. It gives Stage-IV cosmology surveys a single engine for testing how cosmic structure grows when gravity is not pure general relativity.","discovery_kind":"new_method","skeptic_critique":{"model":"moonshotai/kimi-k3","headline":"The ~1% large-scale suppression vs linear theory is attributed to physical Vainshtein mode-coupling, but the Appendix A diagnostic cannot distinguish that from a discretization error proportional to the nonlinear term — an error that would be shared by the whole ECOSMOG-family solver lineage used as","rationale":"I read the paper in good faith: the unification into one master Vainshtein equation with three background functions is real, cleanly derived work, and the validation program (paired-phase ICs, QCDM baselines to isolate background effects, an appendix honestly investigating the large-scale mismatch, disclosure of the parallel ecosmog-eft effort) is careful and credibly executed. The reader's flagged QSA limitation is genuine but is a stated scope boundary, not a hidden assumption — every comparison is made within the QSA regime, and the clustering-DE exclusion (M₄²) is openly acknowledged. The sharper soft spot is epistemic: the validation architecture is dominated by codes sharing the same solver lineage and discretization, so code-to-code agreement demonstrates regression consistency more than correctness. The one place where the code departs from an external reference — linear theory on large scales — is precisely where the independent code (HiCOLA) does not, and the paper's \"inherent mode-coupling\" interpretation rests on a diagnostic (R_c² scaling) structurally incapable of separating continuum physics from nonlinear-term discretization error. The amplitude is small (~1%), so this does not overturn the central \"unified solver works\" claim, and the authors' good-faith investigation counts in their favor. But for a paper whose purpose is percent-level Stage-IV predictions, a ~1% effect on BAO scales with an unsettled physical-vs-numerical origin warrants one cheap, decisive test before full acceptance. Hence CONDITIONAL: accept subject to the resolution-convergence demonstration. Not UNCHANGED, because the reader's ACCEPT/HIGH did not grapple with the intra-family validation circularity or the non-decisive nature of the Appendix A test; not REJECT, because the anomaly is small, disclosed, and plausibly physical.","tokens_in":34491,"tokens_out":3502,"duration_ms":111798,"concrete_test":"Repeat the Appendix A no-AMR nDGP diagnostic (L=1024 h⁻¹Mpc, identical ICs/phases, z=0) at base-grid resolutions N_g=512³, 1024³, 2048³ (4096³ if feasible), holding all solver settings fixed, and measure the suppression amplitude Δ of P_MG/P_ΛCDM relative to linear theory at k<0.05 h/Mpc. If Δ plateaus at ~1% independent of N_g, the mode-coupling interpretation is confirmed. If Δ decreases with resolution (consistent with the truncation order of the second-derivative stencil), the mismatch is a discretization artifact and the large-scale accuracy claim must be revised. As an independent cross-check, compute the expected long-mode suppression analytically at one-loop from the master equation's nonlinear term and compare its magnitude to the simulated Δ.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The strongest claim rests on \"validated\" 1–2% accuracy of nonlinear P(k). But the validation set is mostly intra-family: legacy ECOSMOG-V (the parent code), the GCCG ECOSMOG variant (same lineage, in-prep collaborators), and ecosmog-eft/mg-glam (same grid-relaxation algorithm class). The one fully independent code, HiCOLA, is also the one that does NOT exhibit the paper's most notable anomaly: the ~1% scale-independent suppression at k≲0.05 h/Mpc relative to linear theory. The paper reads this as \"HiCOLA does not solve the master equation, so it misses real mode-coupling physics.\" The alternative reading — that the ECOSMOG-family codes share a discretization artifact in the nonlinear Vainshtein operator — is not excluded by anything shown. Specifically, the Appendix A test scales R_c² and shows the mismatch grows/shrinks with the nonlinear term's strength. That demonstrates sensitivity to the nonlinear term, but a discretization error in the operator-split finite-difference representation of (∇²φ)²−(∂i∂jφ)² would also scale linearly with R_c² at leading order. The known-delicate Chan & Scoccimarro operator splitting makes a term-proportional discrete error plausible, and the reported convergence tests varied solver parameters (V-cycles, sweeps, initial guess) but not the base grid resolution, which is the one axis that discriminates continuum physics from mesh error. If the suppression is an artifact, the code's absolute accuracy on BAO-relevant scales — the scales that matter most for the stated Stage-IV purpose — is worse than claimed, and intra-family code agreement cannot reveal it. This is more load-bearing than the reader's QSA concern, which is an explicitly stated scope restriction with all comparisons made inside that regime.","agreement_with_reader":"partial"},"referee_report":{"model":"moonshotai/kimi-k3","summary":"The authors present EFT-RAMSES, an extension of the ECOSMOG/RAMSES N-body code that embeds the EFTofDE framework (in both the original EFT-function and α-basis parameterisations) into a single \"master\" Vainshtein equation (Eq. 27) with three time-dependent coefficients (α, β, R_c²). Under the quasi-static and weak-field approximations, this one equation covers nDGP/sDGP, cubic scalar and vector Galileons, GCCG, and generic EFT models, so a single multigrid Newton–Gauss–Seidel solver serves all of them. The code is validated with 1024³-particle, 1 Gpc/h simulations of nDGP, csG, GCCG, and two EFT models, compared against legacy ECOSMOG-V, an independent GCCG ECOSMOG variant, and the independent HiCOLA code, finding ~1–2% agreement on nonlinear scales and the expected Vainshtein screening turnover. A persistent ~1% scale-independent suppression relative to linear theory at k≲0.05 h/Mpc is interpreted in Appendix A as physical mode-coupling driven by the nonlinear Vainshtein term, based on diagnostics that rescale R_c² and vary relaxation parameters.","tokens_in":34861,"tokens_out":2893,"duration_ms":55665,"significance":"If the validation holds, this is a useful and timely tool: a publicly released, model-agnostic nonlinear solver for the full class of Vainshtein-screening Horndeski theories, which removes the need to hard-code model-specific scalar-field equations and is directly relevant to Stage-IV survey modelling. Strengths worth naming: the master-equation reduction (Eqs. 27–28) is a genuine reparameterisation validated against independent solvers rather than against quantities derived from itself; the validation is multi-code (legacy ECOSMOG-V, an independent GCCG ECOSMOG implementation, HiCOLA) and multi-redshift; QCDM counterpart runs cleanly separate background-expansion from fifth-force effects; the csG comparison uses paired inverted-phase ICs to control sample variance; and the code is publicly available. The explicit treatment of the cvG→csG limit (§3.2.4) and the EFT-basis mappings (Eqs. 62–64) add to the paper's usefulness as a reference.","major_comments":[{"comment":"The ~1% scale-independent suppression at k≲0.05 h/Mpc relative to linear theory is asserted to be 'inherent mode-coupling' and the text states the authors 'can confidently rule out it as a code error'. The evidence shown does not support that confidence. The Appendix A diagnostic rescales R_c² and shows the mismatch tracks the strength of the nonlinear term; but a discretization error in the operator-split finite-difference representation of (∇²φ)²−(∂i∂jφ)² (the Chan & Scoccimarro splitting inherited from ECOSMOG-V) would also scale with R_c² at leading order, so this test cannot distinguish continuum mode-coupling from a term-proportional mesh error. The codes exhibiting the effect (legacy ECOSMOG-V, EFT-RAMSES, ecosmog-eft, mg-glam) all share the grid-relaxation/operator-splitting algorithm class, while the one fully independent code, HiCOLA, does not show the anomaly — a fact the pape","section":"§4.3.1 and Appendix A (Figs. A1–A2)"},{"comment":"The mismatch of the longest-wavelength (lowest-k) mode is attributed to 'some version difference that affects the new and old ΛCDM runs, where EFT-RAMSES shows a better behaviour.' This is too vague for a validation paper: the ΛCDM runs should be the most trivially reproducible part of the comparison, and an unexplained discrepancy in the baseline undermines confidence in the ratios built on it. Please identify the cause (IC generator difference — MPGRAFIC vs 2LPTic is a candidate given Table 1 —, background integration, or binning) and state it explicitly.","section":"§4.3.1, Fig. 1 discussion"}],"minor_comments":[{"comment":"Equations (36)–(38) for the cvG model duplicate the equation numbers already used for the nDGP parameters in §3.2.2 (Eqs. 36–38). This is a numbering error that will confuse readers; please renumber.","section":"§3.2.3"},{"comment":"The description of Section 4 is duplicated verbatim ('Section 4 details our computational methodology, outlining the architecture...'). One of the two sentences should be removed or rewritten.","section":"§1, final paragraph"},{"comment":"Typo: 'the csG (red)z and QCDM (orange) models' — stray 'z'.","section":"Fig. 2 caption"},{"comment":"Typo: 'the first efficientlympi parallelised N-body simulation code' — 'efficientlympi' should be 'efficiently MPI-parallelised'.","section":"§4.1"},{"comment":"'the Large Survey of Space Telescope (Collaboration 2012)' should read 'the Large Synoptic Survey Telescope (LSST)'.","section":"§1"},{"comment":"The statement that the validity of the combined QSA+WFA 'has been firmly established by previous counterpart works that successfully benchmarked these approximations against full, un-approximated dynamical simulations' is given without citations at that point; please cite the specific benchmarking studies (e.g., Winther & Ferreira 2015; Barreira et al. 2013b are cited only later, in §5).","section":"§2.3"},{"comment":"The conclusions quote a 1–2% bound on nonlinear-scale deviations, but the figures show only qualitative agreement; a short quantitative statement (e.g., maximum fractional residual between EFT-RAMSES and each comparator over a stated k-range) would make the headline number verifiable. Also, given that the code is public, consider depositing the power-spectrum data in a public repository rather than 'upon request'.","section":"§5 / Data Availability"},{"comment":"All models except csG use a single realisation. Since code-to-code comparisons use identical ICs this is acceptable, but the linear-theory comparisons at low k (the basis for the Appendix A anomaly claim) are subject to sample variance for the single-realisation models; a caveat to this effect would be appropriate.","section":"Table 1"}],"recommendation":"minor_revision","confidential_remarks":"The validation is heavily weighted toward the ECOSMOG code family (legacy ECOSMOG-V, an in-preparation GCCG variant by collaborators, and ecosmog-eft/mg-glam, which share the grid-relaxation algorithm class), with HiCOLA the only fully independent comparator — and the one discrepancy with HiCOLA is interpreted in the paper's favour rather than investigated. I do not think this rises to a correctness problem for the central code-validation claim, but the requested grid-resolution test would substantially strengthen the paper. The coordinated release with the parallel ecosmog-eft paper (Ganjoo et al. 2026) is disclosed appropriately."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a methods paper that does what it claims. They fold the cubic Horndeski/EFT sector into one master Vainshtein PDE controlled by three background coefficients, ship the code, and show nDGP, csG, GCCG and two generic EFT runs produce nonlinear P(k) that match legacy ECOSMOG and HiCOLA at the percent level on the scales they resolve, with the expected screening turnover. That consolidation plus a usable α-basis/CPL path is the real product; the individual model equations were already known.\n\nWhat they do well is the validation design. Same ICs, QCDM counterparts that separate background from fifth force, multi-redshift, and an honest Appendix A that at least tries to diagnose the ~1% large-scale suppression versus linear theory. Code is public. Citations and math look standard and careful inside the stated quasi-static, no-clustering-DE scope. They flag the M4^{2}/cs limitation rather than hide it.\n\nThe soft spot that matters is the anomaly diagnosis. Scaling Rc^{2} shows the mismatch tracks the nonlinear term, but that does not cleanly separate continuum mode-coupling from a discretization error in the operator-split finite-difference form of (∇^{2}φ)^{2}−(∂i∂jφ)^{2}—an error that would also scale with Rc^{2} and would be shared by the whole ECOSMOG-family lineage used as the main cross-check. HiCOLA, the one fully independent code, does not show the offset, and they did not vary base grid resolution in the convergence suite. So absolute accuracy on BAO-relevant large scales is a bit less settled than the abstract implies. That is a real caveat for Stage-IV use, not a reason to discard the work. Novelty is moderate: ecosmog-V already existed, and a parallel ecosmog-EFT paper appeared at the same time (they disclose it).\n\nThis is for people who need nonlinear MG/EFT forecasts or who will actually run the code. It deserves a serious referee. I would engage with it and cite the public tool when I need these runs.","headline":"Solid infrastructure paper: one master Vainshtein solver plus public code and multi-model P(k) checks; the large-scale linear mismatch is real but not cleanly proven physical, and novelty is moderate given the ECOSMOG lineage and a parallel release.","tokens_in":32357,"tokens_out":552,"would_cite":true,"duration_ms":12473,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"One master Vainshtein equation lets a single N-body code simulate many dark-energy and modified-gravity models.","keywords":["effective field theory of dark energy","N-body simulations","Vainshtein screening","modified gravity","Horndeski theory","matter power spectrum","cubic Galileon","DGP"],"falsifier":"Run the same initial conditions with a solver that retains the dropped time derivatives or the M_4^{2} operator; if the nonlinear matter power spectrum then differs from EFT-RAMSES by more than the claimed one-to-two percent on the scales validated here, the master-equation reduction is incomplete.","tokens_in":31986,"feed_emoji":"⭐","tokens_out":905,"duration_ms":16316,"temperature":0.7,"pith_summary":"Stage-IV surveys will map cosmic structure so precisely that background expansion alone cannot tell dynamical dark energy from modified gravity. The authors therefore built EFT-RAMSES, an extension of an existing adaptive-mesh N-body code that embeds the effective field theory of dark energy. Diverse scalar- and vector-tensor theories are reduced to one master Vainshtein equation controlled by three time-dependent coefficients. High-resolution runs of normal-branch DGP, cubic Galileon, generalised cubic covariant Galileon and generic EFT models recover the expected screening turnover and match legacy and independent codes to roughly one-to-two percent on nonlinear scales. The result is a single, publicly available engine that can specialise to many models without rewriting the solver, ready for precision tests with forthcoming survey data.","feed_headline":"One equation runs many dark-energy N-body models","feed_subtitle":"A master Vainshtein solver matches legacy codes and recovers screening for DGP, Galileons and EFT","key_machinery":"The master Vainshtein equation: a single nonlinear elliptic equation for the scalar-field perturbation, written in code units, whose model-specific content is entirely encoded in three time-dependent coefficients α, β and R_c².","core_discovery":"By consolidating the normal and self-accelerating DGP branches, cubic scalar and vector Galileons, the generalised cubic covariant Galileon and generic EFT parameterisations into a single master Vainshtein equation whose physics is carried by three time-dependent background functions, EFT-RAMSES produces nonlinear matter power spectra that agree with both its parent code and an independent approximate code while correctly recovering Vainshtein screening.","pith_inferences":["Once the quasi-static restriction is lifted, the same master-equation architecture could be reused for clustering dark-energy models that current Stage-IV analyses may need.","The observed large-scale power suppression relative to linear theory, shown to be driven by nonlinear mode coupling, may itself become a diagnostic of Vainshtein-type screening in survey data.","Vector-tensor models already covered by the master equation open a route to testing whether longitudinal vector modes leave distinct nonlinear signatures compared with pure scalar Galileons."],"forward_implications":["A single public code base can generate nonlinear predictions for nDGP, cubic Galileons, GCCG and generic α-basis EFT models without model-specific solvers.","Background expansion and fifth-force effects can be cleanly separated by comparing full runs against QCDM counterparts that share the same expansion history.","The same pipeline can produce halo mass functions and weak-lensing maps deep into the nonlinear regime for Stage-IV survey forecasts.","Parameter-space scans over α_M and α_B become feasible because only the three background coefficients need updating."],"fun_headline_variants":["Master Vainshtein equation unifies DGP, Galileons and EFT N-body runs","One solver handles nDGP, cubic Galileons and generic EFT dark energy","EFT-RAMSES embeds EFTofDE α-basis into a single Vainshtein engine","Consolidated master equation recovers screening across DE and MG models","High-res N-body spectra match legacy codes for DGP, csG, GCCG and EFT"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The quasi-static and weak-field approximations drop all time derivatives of the scalar and metric perturbations, so the equations never see dark-energy sound-speed operators and cannot describe models in which dark energy itself clusters.","fun_headline_variants_meta":{"raw":{"variants":["Master Vainshtein equation unifies DGP, Galileons and EFT N-body runs","One solver handles nDGP, cubic Galileons and generic EFT dark energy","EFT-RAMSES embeds EFTofDE α-basis into a single Vainshtein engine","Consolidated master equation recovers screening across DE and MG models","High-res N-body spectra match legacy codes for DGP, csG, GCCG and EFT"]},"model":"grok-4.5","effort":"low","cost_usd":0.004519,"raw_usage":{"total_tokens":1445,"prompt_tokens":929,"num_sources_used":0,"completion_tokens":101,"cost_in_usd_ticks":45188000,"prompt_tokens_details":{"text_tokens":929,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":415,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":929,"tokens_out":101,"duration_ms":8456,"temperature":1.0,"reasoning_tokens":415,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T05:23:20.216346+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Run the same initial conditions with a solver that retains the dropped time derivatives or the M_4^{2} operator; if the nonlinear matter power spectrum then differs from EFT-RAMSES by more than the claimed one-to-two percent on the scales validated here, the master-equation reduction is incomplete.","supporting_citations":[],"review_version":1}