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REVIEW 3 major objections 5 minor 1 cited by

Constraints on multi-fluid cosmology in modified Gauss-Bonnet gravity models with different observational data sets

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Three f(G) gravity models fit the same cosmic data as ΛCDM.

desk verdict A standard MCMC pipeline applied to f(G), but the background is assumed rather than derived and the growth equation looks dimensionally inconsistent; the viability claim does not hold. read the letter →

arxiv 2507.22191 v2 pith:H55LDIZA submitted 2025-07-29 gr-qc

Praveen Kumar Dhankar , Albert Munyeshyaka , Aritra Sanyal , Safiqul Islam , Farook Rahaman This is my paper
classification gr-qc
keywords modifiedGauss-Bonnetgravityf(G)multi-fluidcosmologystructuregrowthredshift-spacedistortionfσ8dataMarkovChainMonteCarlocosmologicalparameterconstraints
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

These authors set out to show that modified Gauss-Bonnet gravity—a theory in which the Einstein action gains an arbitrary function of the Gauss-Bonnet curvature invariant $G$—can account for both the accelerated expansion and the growth of cosmic structure without a cosmological constant. They take three $f(G)$ functional forms, fit them to Hubble, BAO, and redshift-space distortion data with Markov Chain Monte Carlo, and report that all three pass both background and perturbation constraints. The reason this would matter is that $f(G)$ gravity would remain a physically motivated alternative to $\Lambda$CDM, and the growth fits return $\sigma_8 \approx 0.64$, a value compatible with the low-redshift large-scale structure data. The paper does not claim to beat $\Lambda$CDM; it claims to remain observationally viable alongside it.

What carries the argument

The machinery is a chain of three equations. The background is set by the modified Friedmann equation $3H^2 = \frac{1}{2}(G f' - f - 24\dot G H^3 f'') + \rho_m$, with Gauss-Bonnet energy density and pressure defined so that $f(G)=G$ recovers general relativity. Structure growth is carried by a linear overdensity equation from the authors' earlier covariant treatment; its quasi-static dust limit becomes the growth equation, and combining the growth rate with the clustering amplitude yields the $f\sigma_8$ observable that the redshift-space distortion data constrain. The third piece is the power-law scale-factor ansatz $a(t)=a_0 t^m$, which turns the modified Friedmann equation into a closed-form $H(z)$ and lets every model be fitted with MCMC. That ansatz is what makes the constraints computable, and it is also the load-bearing simplification.

What would settle it

Take the best-fit parameters from Table 1 for any of the three models, solve the modified Friedmann equation directly for $H(z)$ without imposing $a(t)=a_0 t^m$, and re-run the same CC, BAO, and $f\sigma_8$ likelihoods; if the solved expansion shifts the best-fit parameters or the predicted $f\sigma_8$ by more than the reported $1\sigma$ ranges, the constraints are an artifact of the power-law assumption.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central result is that perturbation-level data do not rule out modified Gauss-Bonnet gravity. Using the modified Friedmann equation and a growth equation obtained from the quasi-static limit of a covariant perturbation equation, the authors run MCMC fits for three $f(G)$ forms—a general model, a power-law model, and an exponential model—against $H(z)$, BAO, and $\sigma_8+f+f\sigma_8$ data. The best-fit parameters in Table 1 show all three models tracking the $\Lambda$CDM expansion history while producing $\sigma_8$ near $0.64$ from the growth sector. From this they conclude that the models are observationally viable at both background and perturbation levels and are plausible alternatives to general relativity with a cosmological constant.

Load-bearing premise

The load-bearing premise is that the universe's expansion follows the power-law scale factor $a(t)=a_0 t^m$, so the Hubble history is imposed rather than solved from the modified gravity equations; if the true $f(G)$ dynamics predict a different expansion, the reported parameter constraints and the viability claim do not follow.

Editorial extensions

If this is right

  • If the central claim is right, modified Gauss-Bonnet gravity is not excluded by current data, so $f(G)$ remains a viable dark-energy-free explanation of late-time acceleration.
  • The fitted $\sigma_8 \approx 0.64$ implies the growth tension seen in $\Lambda$CDM is softened: low-redshift structure-growth data can be matched without invoking a different matter density.
  • Joint $H(z)$+BAO fits tighten the parameter space and reveal which parameter combinations are degenerate, so future independent distance or growth measurements can break those degeneracies.
  • Because all three models reduce to $\Lambda$CDM in particular limits, the constraints quantify how far $f(G)$ may deviate from general relativity while still fitting observations.
  • The same fitting procedure can be applied to other $f(G)$ functional forms as a screening step before more expensive full perturbation checks.

Reading between the lines

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

  • Inference: because the constraints never solve the full $f(G)$ Friedmann dynamics, the reported parameter values are conditional on the power-law background; a full solution could shift the best fit and might change the $\sigma_8$ conclusion.
  • Inference: the same data could support a formal model-comparison test—e.g., information criteria or Bayesian evidence against $\Lambda$CDM—to decide whether the extra $f(G)$ parameters are warranted.
  • Inference: the growth constraints inherit the quasi-static approximation, so verifying Equation (2.12) against the full covariant perturbation system would materially strengthen the viability claim.
  • Inference: applying the identical pipeline to $f(G)$ forms already known to be ghost-free or to pass solar-system tests would separate which of the three models is physically safe, since this paper does not establish those conditions.
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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

3 major / 5 minor

Summary. The paper studies three phenomenological f(G) gravity models (a general model A, a power-law model B, and an exponential model C) in a multi-fluid FRW cosmology. It states a modified Friedmann equation (2.7) and a structure-growth equation (2.17), and then uses MCMC with cosmic-chronometer H(z), BAO, and f-sigma8 data to constrain the model parameters. The central claim is that, with best-fit parameters, all three models can fit the background and growth datasets and thus represent viable alternatives to Lambda-CDM.

Significance. If the constraints were reliable, the paper would provide a useful observational assessment of f(G) gravity at both background and perturbation levels. The authors do apply a standard MCMC pipeline (emcee, GetDist) and assemble CC, BAO, and RSD data, which is a reasonable approach in principle. However, the central methodological chain is broken: the background expansion history is not derived from the f(G) field equations, and the growth equation is imported without derivation. These two issues affect every reported constraint, so the stated significance is conditional on redoing the analysis, which is not a minor fix.

major comments (3)
  1. [Section 4, eq. (2.7)] The background H(z) is not obtained by solving the modified Friedmann equation (2.7). The text says that H(z) is obtained under the assumption of a power-law scale factor a(t)=a0 t^m, which fixes H(z)=H0 (1+z)^{1/m}. This is a purely kinematic one-parameter power law; inserting it into eq. (2.7) gives at most an algebraic consistency condition, not a solution for the f(G) dynamics. Consequently, the constraints on (Omega_m, H0, m, A) in Table 1 and the conclusion that the models provide viable fits to the expansion history do not test the f(G) gravity models. The authors never show the residual of eq. (2.7) for the assumed background, so the claimed background-level viability is not established.
  2. [Section 2.2, eqs. (2.12), (2.17)] The growth equation (2.17) is asserted to follow from the perturbation equation (2.12) and the definition of y in eq. (2.14), but no derivation is given; it is imported from the authors' earlier work [55]. This is load-bearing because all perturbation-level constraints, including the reported sigma8 values, depend on this equation. In addition, as written, the terms inside the braces of eq. (2.17) mix incompatible dimensions (e.g., 1/(12H^3), G/(6H), and (1+z)H'), so the equation cannot be evaluated consistently unless H is explicitly treated as dimensionless or a specific unit system is specified. The authors need either to derive the equation or to show its consistency, and to state the units used in the numerical implementation.
  3. [Section 3 and Table 1] The dataset combination labelled 'sigma8+f+fs8' is not defined. Section 3 lists only the CC, BAO, and 'fs8' data sets; there is no separate description of a direct f(z) or sigma8(z) compilation, although the abstract and Section 4 repeatedly refer to 'sigma8+f+fs8'. Table 1 also omits the G0 parameter for Model C and inconsistently reports parameters such as A for Model A without explaining its treatment in the joint fit. As a result, the constraints in the fourth column of Table 1 cannot be reproduced or interpreted.
minor comments (5)
  1. [Section 2.2, Model A definition] The expression for the coefficient A in the general f(G) model is corrupted and unreadable (the formula involving '4+m[3m(1+w)...]'); the reader cannot implement or verify the model.
  2. [Section 4, paragraph after Fig. 3] The text first states that the authors 'numerically solve the modified Friedmann equation' and then, in the very next sentence, says the evolution is obtained under the assumption of a power-law scale factor. This is contradictory and should be clarified.
  3. [Section 3, data set description] The f-sigma8 data set is described only by citing ref. [20] for 30 samples; the actual compilation, including the covariance or individual data points, is not provided, which makes the MCMC analysis difficult to reproduce.
  4. [References] Reference [55] is cited as the source of the growth equation and described as a multifluid f(G) perturbation analysis, but the listed title 'Instability of 1-loop superstring cosmology' does not match that description; please verify the citation.
  5. [Table 1, sigma8+f+fs8 columns] For Models A and B, the reported Omega_m values close to 1 and sigma8 around 0.64 are far from the Planck-based expectation and from the background fits in the same table; these discrepancies are not discussed and need comment.

Circularity Check

3 steps flagged · score 6.0 of 10

Background H(z) is imposed by a power-law ansatz rather than derived from f(G), so the Model A background constraint reduces to fitting the assumed kinematics; the growth equation is imported from the authors' own prior work.

  1. self definitional [Section 2.2, model A definition; used with the power-law background assumption in Section 4]
    "The general f(G) gravity model (model A) is given by [2,55,88,89] f(G)=G− 1/2 [sqrt(6m(m−1)G/(m+1)^2) + A G^{3/[4m(1+w)]}], where A = 8ρ0(m−1)[13824m^9(m−1)^3]^{−1/[4m(1+w)]}[4+m(3m(1+w)(w+4/3)−18w−19)]"

    A is defined as a prescribed function of m and ρ0, which is the reconstruction condition making the power-law background a(t)=a0 t^m an exact solution of the modified Friedmann equation (2.7) with ρ_m=ρ0 t^{−3m(1+w)}. Section 4 then states that H(z) is obtained 'under the assumption of a power-law scale factor a(t)=a0 t^m', so H(z)=H0(1+z)^{1/m} is an input, not a derived consequence of f(G). For Model A the MCMC fit of m to H(z) and BAO therefore constrains the power-law exponent that was put in, and the background agreement is satisfied by construction. For Models B and C the Table 1 parameter vectors (Ωm,H0,α,β,σ8) and (Ωm,H0,α,p,G0,σ8) contain no power-law index, so the assumed H(z) is an external kinematic input rather than a prediction of the fitted f(G) forms.

  2. fitted input called prediction [Section 4, fσ8 analysis and Fig. 13]
    "These predictions are then directly compared with a comprehensive compilation of RSD data, showing good agreement under appropriate parameter choices as presented in Fig.(13)."

    The 'appropriate parameter choices' are the MCMC best-fit values obtained from the same RSD, fσ8 and σ8 data (Table 1). Thus Fig. 13 displays the in-sample best fit used for parameter estimation, presented as a 'prediction'; the later conclusion that the models 'are capable of fitting the current cosmological datasets' is a restatement of the fit rather than an independent test. This is a mild form of circularity because a poor fit would still have been possible, but the agreement is not out-of-sample evidence for f(G).

1 more flagged steps
  1. self citation load bearing [Section 2.2, eqs. (2.12) and (2.17)]
    "Following the work conducted by Munyeshyaka A et al. [55], the covariant formalism was used and perturbation equations were obtained. In this work we use the obtained perturbation equation in the quasi-static approximation limit and represent it here with some modification as..."

    The structure-growth equation (2.17), on which all σ8 and fσ8 constraints rest, is not derived in this paper but imported from the authors' own prior paper [55] and merely 'represented with some modification'. The conclusion confirms this: 'In a previous paper by Munyeshyaka et al [55], we considered theoretical part on multi-fluid cosmology.' Since [55] is a same-group result that is not machine-checked or independently reproduced in this work, the perturbation-level claim inherits its central equation from a self-citation; the external RSD data give independent grounding, so this is load-bearing but not fully circular.

full rationale

The clearest circularity is in the background sector. Section 4 says the modified Friedmann equation is solved, but then immediately says H(z) is obtained from an assumed power-law scale factor a(t)=a0 t^m. For Model A, m is both the power-law exponent and the f(G) parameter, and A is prescribed in terms of m and ρ0, so the power-law background satisfies eq. (2.7) by construction; fitting m to H(z)/BAO recovers the assumed kinematics rather than testing f(G). For Models B and C, no power-law index appears in the fitted parameter vectors, so the H(z) entering the BAO distances and the growth equation is an external kinematic input, not a consequence of the fitted f(G) forms. At the perturbation level, eqs. (2.12) and (2.17) are taken from the authors' own prior work [55] rather than derived, making the σ8/fσ8 constraints depend on a self-citation; additionally, Fig. 13 compares best-fit curves to the same RSD data used in the MCMC, so it is an in-sample fit presented as a prediction. The external H(z), BAO and RSD data sets still provide genuine information and a model could fail these comparisons, so the paper is not wholly circular; nevertheless the central background claim is true by construction and the perturbation claim leans on a self-cited equation, giving a partial-circularity score of 6.

Assumptions & free parameters 11 free parameters · 6 assumptions · 0 invented entities

The paper's central claim rests on several unverified assumptions: a fixed power-law background that bypasses the f(G) dynamics, a perturbation equation taken from the same group's prior work, and unstated MCMC priors. The models introduce many fitted parameters with no independent predictions, and no new physical entities are introduced.

free parameters (11)
  • H0 = 60.0 (CC+BAO); 66.2 (CC)
    Hubble constant fitted to H(z) and BAO data in every dataset combination.
  • Ωm = 0.30 (CC); 1.0 (fs8 Model A)
    Matter density parameter fitted in all analyses; boundary value in fs8 fit suggests degeneracy.
  • m (Model A) = 1.082 (CC); 2.5 (fs8)
    Power-law exponent in model A and in the background ansatz a(t)=a0 t^m.
  • A (Model A) = 0.10 (CC); 0.0010 (fs8)
    Amplitude of the second correction term in model A; fitted in MCMC.
  • α (Model B) = 1.0 (CC); 0.014 (fs8)
    Amplitude of power-law f(G)=α G^β.
  • β (Model B) = 1.0 (CC); 1.92 (BAO); 0.53 (fs8)
    Exponent of power-law f(G).
  • α (Model C) = 0.18 (CC); 0.01 (fs8)
    Amplitude of exponential f(G)=α G0 (1−exp(−p G/G0)).
  • p (Model C) = 0.999 (CC); 2.0 (fs8)
    Exponent in exponential f(G); ΛCDM recovered for large p, but best fits give p around 1 to 2.
  • G0 (Model C) = not reported
    Listed as a free parameter in the model C vector (Section 4) but absent from the results table.
  • σ8 = 0.6444 (Model A fs8)
    Amplitude of matter fluctuations fitted in the σ8+f+fs8 analysis.
  • rd = not reported
    Sound horizon at drag epoch; Section 3 says it is treated as free but its constraints are not shown in Table 1.
assumptions (6)
  • domain assumption The universe is described by a flat FRW metric with dust matter (w=0)
    Stated in Section 2.1 and the abstract; standard but not tested here.
  • domain assumption Quasi-static approximation is valid for the perturbation equations on sub-horizon scales
    Section 2.2 and Section 4: 'QSA is valid on sub-horizon scales and simplifies the analysis'; no scale cut-off is applied to data.
  • ad hoc to paper The scale factor follows a power law a(t)=a0 t^m for the background
    Section 4: 'The evolution of the Hubble parameter H(z) is obtained under the assumption of a power-law scale factor...'; this substitutes for solving the modified Friedmann equation.
  • domain assumption The perturbation equation (2.12) from Munyeshyaka et al. [55] is correct
    Section 2.2: 'we use the obtained perturbation equation... represent it here with some modification'; the equation is not re-derived and may contain dimensional inconsistencies.
  • standard math The algebraic step from eq. (2.12) to the growth equation (2.17) is correct
    Stated as 'Using eq. (2.14) in eq. (2.12) and eq. (2.13) we obtain' with no intermediate steps shown.
  • ad hoc to paper MCMC priors are adequately chosen
    Priors are mentioned in Section 3 but their ranges are never stated, so posterior boundary values cannot be interpreted.

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Cite this review

Pith. "Pith review of Constraints on multi-fluid cosmology in modified Gauss-Bonnet gravity models with different observational data sets." pith.science (2026). https://pith.science/paper/H55LDIZA

@misc{pith2026250722191,
  author       = {Pith},
  title        = {Pith review of: Constraints on multi-fluid cosmology in modified Gauss-Bonnet gravity models with different observational data sets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H55LDIZA}},
  note         = {Machine review of arXiv:2507.22191}
}
read the original abstract

In the present work, we incorporate redshift-space distortion measurement to investigate the growth of large scale structure within the framework of multi-fluid cosmology in the context of modified Gauss-Bonnet gravity. Using three different modified Gauss-Bonnet gravity models, we compare the predictions of modified Gauss-Bonnet gravity expansion history-through the Friedmann equation with Hubble and BAO data sets and constrain models parameters. Within the context of multi-fluid cosmology in modified Gauss-Bonnet gravity, we obtain the structure growth equation. This equation is then combined with Sigma_8 to get f_Sigma_8 predictions-which is compared with redshift-space distortion data to constrain models parameters to obtain best-fit values including Sigma_8. This involves performing a Markov Chain Monte Carlo (MCMC) analysis for these specific forms of modified Gauss-Bonnet models.

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Forward citations

Cited by 1 Pith paper

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