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REVIEW 5 major objections 5 minor 67 references

Fullshape power spectrum for the Symmetron modified gravity model

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The Symmetron model can be fitted to the full-shape galaxy power spectrum: a fast kernel approximation keeps one-loop multipoles within 1% out to $k = 0.17\,h\,\mathrm{Mpc}^{-1}$, and mock catalogues recover general relativity.

desk verdict Useful extension of the group's fkPT machinery to Symmetron, but the validation is internal and the QSA is unproven; the abstract overstates readiness for real data. read the letter →

arxiv 2506.09304 v3 pith:R45ULQF4 submitted 2025-06-11 astro-ph.CO gr-qc

Gerardo Morales-Navarrete , Jorge L. Cervantes-Cota This is my paper
classification astro-ph.COgr-qc PACS 98.80.-k04.50.Kd
keywords symmetronmodifiedgravityfullshapegalaxypowerspectrumscale-dependentgrowthratefkPTapproximationredshiftspacedistortionsone-loopperturbationtheoryMCMCparameterinferenceEZMocksvalidation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper's goal is to make the Symmetron model, a screened scalar-tensor theory of modified gravity, ready for full-shape analysis of galaxy clustering, using the same one-loop perturbation-theory machinery with redshift-space distortions, bias, and effective-field-theory counterterms routinely applied to $\Lambda$CDM. Its central methodological claim is that the fk-kernel approximation, which keeps the scale dependence of the linear growth rate $f(k)$ inside otherwise standard kernels, works for the Symmetron: with counterterms included, the monopole and quadrupole differ from the exact one-loop result by less than 1% for $k < 0.17\,h\,\mathrm{Mpc}^{-1}$. On the physics side, the paper finds that the Symmetron growth rate is nearly indistinguishable from the Hu-Sawicki F6 model in the interval $0.01 \le k \le 0.1\,h\,\mathrm{Mpc}^{-1}$ at viable redshifts, and offers a three-parameter analytic form $f(k) = c_1\tanh^2(c_2 k) + c_3$ that matches both models to better than 0.6%. The payoff, if the claims hold, is a pipeline that recovers the cosmological parameters of general relativity from mock galaxy catalogues when the Symmetron coupling is free, which the authors take as license to apply the model to real survey data.

What carries the argument

The load-bearing device is the fkPT approximation: the one-loop Eulerian kernels $F_2, G_2, F_3, G_3$ are evaluated at their large-scale limit, with the coefficients $A, B$ set to their $k \to 0$ values $A_{LS}, B_{LS}$, so that all scale dependence enters through the linear growth rate $f(k)$ obtained from the modified-growth differential equation, while the discarded short-scale kinematics are absorbed by the EFT counterterms $\alpha_0, \alpha_2$ at the level of the multipoles. This converts expensive mode-by-mode kernel evaluations into fast FFTLog loop integrals, which is what makes an MCMC fit feasible. The scale dependence that fkPT preserves comes from the Symmetron's modified Poisson factor $\mu(k,a) = 1 + \frac{2\beta^2(a)}{A(\phi)}\frac{k^2}{k^2 + a^2 m^2(a)}$, with the phase-transition tracking solution $\phi(a) = \phi_0\sqrt{1 - (a_{\rm ssb}/a)^3}$ at $a_{\rm ssb} = 1/2$; the nonlinear kernels $M_2, M_3$ encoding the screening and anti-screening mechanisms come from the perturbative screening formalism, and the RSD multipoles come from an expansion of the velocity-moments generating function with an infrared-resummed linear power spectrum.

What would settle it

Compare the fkPT one-loop redshift-space multipoles for the Symmetron at the paper's fiducial parameters ($\beta_0 = 1$, $m_0 = 1$, $a_{\rm ssb} = 0.5$) against N-body simulations that evolve the scalar field without the quasi-static approximation; if the monopole or quadrupole differ by more than about 1% for $k < 0.17\,h\,\mathrm{Mpc}^{-1}$, the fkPT validation that the pipeline claim rests on would not transfer to the real model. A cheaper direct check is to recompute the paper's cross-section behind Fig. 5: the agreement within 1% is only reached after adding the counterterms $\alpha_0, \alpha_2$, so verifying that the counterterm values required near $k = 0.17\,h\,\mathrm{Mpc}^{-1}$ are consistent with EFT power counting, rather than anomalously large, would settle whether the approximation is genuine or effectively fitted.

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Extended reading notes

Core claim

On its own terms, the paper establishes three connected results. First, the scale-dependent growth rate of the Symmetron model closely tracks that of the $n=1$ Hu-Sawicki F6 model for $0.01 \le k \le 0.1\,h\,\mathrm{Mpc}^{-1}$ and at redshifts where the model is observationally viable, with deviations from $\Lambda$CDM peaking near $z \approx 0.5$ and staying below about 2% on the scales studied; the proposed parametrization $f(k) = c_1\tanh^2(c_2 k) + c_3$ reproduces both models with a maximum deviation below 0.6% up to $k = 0.2\,h\,\mathrm{Mpc}^{-1}$. Second, the fkPT approximation is viable for the Symmetron: when the fk kernels are evaluated at the large-scale limit of the kernel coefficients and the EFT counterterms $\alpha_0$, $\alpha_2$ are included, the relative difference against the full-kernel computation stays below 1% for both monopole and quadrupole up to $k = 0.17\,h\,\mathrm{Mpc}^{-1}$. Third, an MCMC implementation of the resulting multipoles, fitted to the mean of seven EZMock catalogues at $z = 0.75$ with a flat prior on the coupling, drives the Symmetron coupling to $\beta_0 < 3.8 \times 10^{-7}$ while recovering the simulation's cosmological parameters within $1\sigma$; the authors conclude the pipeline is ready for cosmological parameter inference with real data. The paper also reports a correction to earlier $f(R)$ results: using $f(k)$ instead of $f_0$ in the infrared resummation boosts the predicted power, most visibly in the quadrupole, and the change cannot be absorbed by re-tuning counterterms for both multipoles simultaneously.

Load-bearing premise

The load-bearing premise is the quasi-static approximation for the Symmetron scalar field, used to derive the modified Poisson equation on which every nonlinear prediction rests (Section 4.1, after eq. 4.2); the paper cites work showing that dropping this approximation changes the matter distribution through the fifth force, but does not establish that the approximation holds on the scales fitted here.

Editorial extensions

If this is right

  • The fkPT-plus-counterterms scheme is a valid substitute for the full one-loop kernels in Symmetron analyses up to $k = 0.17\,h\,\mathrm{Mpc}^{-1}$, which is the scale range the paper recommends for MCMC fits.
  • Because the Symmetron and F6 multipoles are nearly degenerate, constraints derived for F6-type scale-dependent growth can be approximately translated into the Symmetron parameter space ($\beta_0$, $m_0$, $a_{\rm ssb}$) on these scales.
  • The analytic growth parametrization can replace solving the growth differential equation inside the nonlinear kernels, saving computation time in parameter inference for both the Symmetron and F6 models.
  • Earlier $f(R)$ full-shape predictions computed with $f_0$ in the infrared resummation should be re-evaluated, since the $f(k)$ version raises the predicted power and no single counterterm choice reproduces both multipoles.
  • The readiness claim applies specifically to the general-relativistic limit: real-data inference with a free Symmetron coupling is the stated next step once fullshape covariances for current surveys become available.

Reading between the lines

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

  • The GR-mock test cannot by itself certify the Symmetron predictions: recovering $\beta_0 \to 0$ from general-relativistic mocks validates the code's limit, not its behaviour at $\beta_0 = 1$, and the paper notes that existing Symmetron simulations are not precise enough for a one-loop RSD comparison; a pointed test would run the same full-shape pipeline against a Symmetron simulation at the paper'
  • If the quasi-static approximation fails at the fitted wavenumbers, the fkPT validation is void because the kernels derive from the quasi-static Klein-Gordon equation; the paper flags the concern through its own citations but does not quantify it for the adopted Symmetron parameters.
  • The success of the $\tanh^2$ growth parametrization for two different screening models hints that the same form may fit other screened theories such as dilaton or chameleon models with individually fitted constants, which the paper does not investigate.
  • Because Symmetron and F6 are nearly degenerate on these scales, a real-data fit may yield a bound on a combined screened-deviation amplitude rather than an isolated detection of the Symmetron phase transition; separating the models would likely require the bispectrum or smaller-scale information beyond the current one-loop pipeline.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. This paper constructs a full-shape, redshift-space galaxy power spectrum model for the Symmetron modified-gravity model by implementing scale-dependent growth and the fkPT approximation in the FOLPS-nu code. It compares the Symmetron growth rate with the n=1 Hu-Sawicki F6 model, proposes a three-parameter fitting formula for f(k), computes one-loop IR-resummed RSD multipoles with EFT counterterms, and validates the code by fitting GR EZMocks, recovering Lambda-CDM parameters with an upper bound on the Symmetron coupling beta0. The abstract concludes that the pipeline is ready for cosmological parameter inference with real data.

Significance. The paper's main contribution is a fast numerical pipeline for full-shape Symmetron power spectra, including a correction to the IR-resummation that uses f(k) instead of f0. The growth parametrization and the publicly available codes are useful resources, and the EZMock recovery of GR parameters is a sensible sanity check. However, the significance of the scientific claims is currently limited: the quasi-static approximation is assumed without validation, the only simulation test is in the GR limit beta0 -> 0, and the fkPT accuracy test is internal to the same perturbative framework. If these gaps are filled, the pipeline would be a valuable tool for forecasting and, eventually, for DESI-class data.

major comments (5)
  1. [§4.2, Eq. (4.2)] The quasi-static approximation is assumed when writing the Klein-Gordon equation in the form (3+2w_BD) a^{-2} nabla^2 phi = -8 pi G rho + NL, and this equation underlies all subsequent full and fkPT kernels. The manuscript does not establish the validity of the QSA for the chosen Symmetron parameters (beta0 = 1, m0 = 1, assb = 0.5) over the scales used in the fits (k <= 0.17 h/Mpc). Section 5.1 cites Refs. [19,76] as evidence that QSA affects the matter distribution through the fifth force, and states that no suitable Symmetron simulations exist for validation. As a result, the <1% agreement in Fig. 5 compares two approximations that share the same QSA error, and the predicted Symmetron multipoles may be biased if QSA fails. A quantitative QSA error estimate, a comparison with full time-dependent perturbation theory, or validation against Symmetron N-body simulations is needed before the model can be used for real-data inference.
  2. [§5.1, Fig. 8, Table 1] The EZMock validation only tests the GR limit beta0 -> 0: the fitted upper bound beta0 < 3.8 x 10^-7 and the recovery of Omega_m, h, As, and b1 demonstrate that the pipeline reduces to GR, but they do not test the model's prediction for a nonzero coupling where Symmetron differs from Lambda-CDM. In particular, the fifth-force enhancement and screening terms in the nonlinear kernels are never confronted with data. The conclusion that the pipeline is ready for real-data inference for the Symmetron is therefore not supported by this test; it needs a validation with mock data generated with a nonzero beta0 or with Symmetron N-body simulations.
  3. [§4.4, Fig. 5] The fkPT accuracy test is internal to the same modeling framework: the 'full' kernels are solutions of the same perturbative equations (4.26)-(4.32) with the same QSA and the same growth equation, and the fk approximation is compared with them. This is a legitimate consistency check, but the paper does not state how the counterterms alpha0 and alpha2 used in the dashed curves of Fig. 5 are chosen. If they are fitted to minimize the difference, the <1% agreement is partly by construction and says little about the accuracy of the model relative to the true Symmetron power spectrum. Please specify the counterterm values, whether they are fitted or fixed, and check the approximation against an external standard (e.g., N-body simulations or an emulator).
  4. [§5, Figs. 6 and 7] In the direct multipole comparison, the counterterms are assumed equal to their F6 values ('For simplicity, we decided to assume the same counterterm values for both models'). Since EFT counterterms absorb small-scale physics that differs between models, fixing them to F6 can bias the comparison; the finding that Symmetron and F6 multipoles are similar is then partly enforced by the assumption. The counterterms should be marginalized over or calibrated with Symmetron-specific simulations before drawing conclusions about the similarity of the two models.
  5. [§6 and Abstract] The abstract states that the pipeline is 'ready to make cosmological parameters' inference with real data,' but Section 6 explicitly says that fullshape covariances suitable for DESI DR1 or DR2 are not yet available and that a proper real-data inference is left for future work. The present paper performs mock-data validation only. The conclusion should be tempered to 'the pipeline is ready for application once appropriate covariances and validated nonlinear modeling are available,' or the abstract should be revised to match the actual scope.
minor comments (5)
  1. [Eq. (3.9)] The fitting formula sets c3 = f0 = Omega_m^0.55, but for MG models the relation f = Omega_m^gamma is an approximation; clarify whether c3 is fixed in this way or fitted along with c1 and c2.
  2. [Fig. 4 caption] The labels 'fMG' and 'fp' in the right panel are not defined; please define them in the caption or in the text.
  3. [§4.4, Eqs. (4.49)-(4.50)] The notation 'A=B=ALS' and 'A=B=BLS' is confusing; presumably the intention is to evaluate A and B at their large-scale limits ALS and BLS. Please rewrite.
  4. [Appendix B] The typo 'ec. (3.70)' should be 'eq. (3.70)', and the notations 'fR0' and 'f_R0' are used inconsistently.
  5. [References [17] and [75]] References [17] and [75] appear to be the same paper (Ruan et al., JCAP 05 (2022) 018, arXiv:2110.00328); please merge or disambiguate them.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fkPT check and EZMock GR-limit fits are internal consistency tests, and the unvalidated QSA is a physical validity risk, not a circular reduction.

full rationale

The paper's central derivations are self-contained and do not reduce to their inputs by construction. The growth parametrization (Eq. 3.9) is explicitly fitted to numerical solutions of the linear growth equation (Eq. 3.7); the <0.6% agreement is honestly presented as an approximation, not as an independent prediction. The fkPT viability test (Fig. 5) compares fk kernels against full kernels computed from the same perturbative framework; this is a legitimate internal test of an approximation scheme, and the EFT counterterms are used in their standard role of absorbing short-wavelength differences, rather than being fitted to the target and then renamed as a prediction. The EZMock validation is an external end-to-end consistency check: mock data generated under GR are fit with the Symmetron pipeline, and recovery of β0→0 with GR cosmological parameters verifies that the pipeline reduces to GR in the appropriate limit; the paper does not claim this test validates nonzero-β0 predictions. The quasi-static approximation (Eq. 4.2) is assumed and cited to [33,34], and the paper itself cites [19,76] noting that QSA can affect the matter distribution via the fifth force; however, this is an unvalidated physical assumption or correctness risk, not a circularity, because the derived multipoles do not equal the QSA assumption by construction. Self-citations to [25,43,54] supply the underlying PT framework and fkPT method, but those works are public, independently code-reproducible, and the approximation is re-tested in this paper, so the citations are not load-bearing in a circular way. Overall, no claim reduces to its inputs by definition, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The model relies on the Symmetron action from the literature, plus several fiducial parameter choices and the fkPT approximation. No new entities are introduced.

free parameters (5)
  • beta0 (Symmetron coupling) = 1.0 (fiducial in predictions)
    Set to unity for the multipole predictions in Section 5; only constrained as an upper limit in the EZMock validation.
  • m0 (Symmetron scalar mass) = 1.0 (fiducial)
    Same fiducial choice; not varied in the main predictions.
  • a_ssb (phase transition scale factor) = 0.5 (z=1)
    Chosen as in refs [16,50]; determines when the fifth force activates.
  • growth parametrization c1, c2, c3 = c1=0.265, c2=3.55 (Sym.) or 3.05 (F6), c3=0.5048/0.50485
    Fitted to the numerically solved growth rate f(k,z) to yield eq. (3.9).
  • EFT counterterms alpha0, alpha2, alpha4, ctilde = assumed same as F6 (Table 1 of [43])
    Not fitted to Symmetron data; adopted from F6 due to similarity, which is an assumption.
assumptions (4)
  • domain assumption The quasi-static approximation for the scalar field perturbation reduces the Klein-Gordon equation to a Poisson-like form.
    Invoked in Section 4.1 (after Eq. 4.2) for both MG models; QSA validity is questionable per [19,76].
  • domain assumption A cosmological constant rho_Lambda is added ad hoc to the Symmetron background to match ΛCDM expansion.
    Introduced in Section 2.2 (Eqs. 2.16-2.17) to make the background viable.
  • domain assumption The fk-kernel approximation retains only growth-rate scale dependence in the kernels and absorbs the rest into EFT counterterms.
    Defined in Section 4.4 (Eqs. 4.49-4.50); must be tested model by model, and the paper does so only internally.
  • standard math Standard one-loop perturbation theory equations for the power spectrum and RSD are taken as given.
    Used throughout Section 4.3, based on earlier works [32,43].

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Cite this review

Pith. "Pith review of Fullshape power spectrum for the Symmetron modified gravity model." pith.science (2026). https://pith.science/paper/R45ULQF4

@misc{pith2026250609304,
  author       = {Pith},
  title        = {Pith review of: Fullshape power spectrum for the Symmetron modified gravity model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R45ULQF4}},
  note         = {Machine review of arXiv:2506.09304}
}
abstract

We make use of the perturbation theory for modified gravity models that we developed in previous works and apply it to construct the fullshape galaxy power spectrum for the Symmetron modified gravity model. First, we study the growth rate, that is a scale dependent quantity, and compare our results with those of the $n=1 $ Hu-Sawcki (HS) model, finding that the Symmetron has a growth quite similar to the HS F6 in the wavenumber interval $0.01 \leq k \leq 0.1 $ and for redshifts where Symmetron model is viable. We also propose a growth parametrization that turns to be a good approximation for the HS and Symmetron models, with a deviation less than $0.6 \%$. To compute the RSD multipoles we employ an expansion of the velocity moments generating function that is suitable for general modified gravity models. Later, we apply the fk-Perturbation Theory (fkPT) approximation to reduce the computation time of nonlinear kernels, to find the fullshape galaxy power spectrum for the Symmetron, and study the differences with HS model. The RSD multipoles of the Symmetron result similar to those of the HS F6 model. Next, we integrate this theory to an MCMC sampler and validate our results by fitting our parameters to EZMocks to recover the parameters that bring the model to GR. We found a similar agreement in the model validation between Symmetron and F6 model, recovering the simulation cosmological parameters, and concluding that our pipeline is ready to make cosmological parameters' inference with real data.

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Reviewed August 7, 2026 · model on record in the stance chip above.