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REVIEW 4 major objections 5 minor 98 references

Constraint on Symmetric Teleparallel Gravity with Different Dark energy Parametrizations from DESI DR2 BAO Data

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that a power-law f(Q)=αQ^n gravity model, closed with CPL or BA dark energy, fits DESI DR2 BAO data as well as or better than ΛCDM.

desk verdict The DESI fit is real but the model isn't the f(Q)+matter system claimed: Eq. (20) is off by a factor of two and the fitted H(z) omits matter/radiation, so the comparison against ΛCDM doesn't test what the paper says. read the letter →

arxiv 2507.05975 v1 pith:ZJ3KWIQI submitted 2025-07-08 gr-qc

Rajdeep Mazumdar , Mrinnoy M. Gohain , Kalyan Bhuyan This is my paper
classification gr-qc MSC 83D0583F05 PACS 98.80.-k04.50.Kd95.36.+x
keywords f(Q)gravitysymmetricteleparalleldarkenergyparametrizationCPLBADESIDR2BAOMCMCparameterconstraintslate-timecosmicacceleration
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

This paper asks whether a modified theory of gravity, symmetric teleparallel f(Q) gravity with the power-law form f(Q)=αQ^n, can explain the accelerated expansion of the Universe without a cosmological constant. The authors combine this model with two standard evolving-dark-energy equations of state, the CPL and BA forms, and fit the background expansion history H(z) to DESI DR2 BAO data plus earlier BAO measurements. They find that both combinations reproduce the data with chi-squared, AIC, and BIC statistics that are better than or competitive with ΛCDM, and that the new DESI DR2 data tighten the parameter constraints and shift low-redshift behavior toward a phantom-like effective equation of state. If the result holds, the geometric dark energy of f(Q) gravity remains a credible alternative to ΛCDM for late-time acceleration.

What carries the argument

The central object is the power-law f(Q)=αQ^n model in symmetric teleparallel gravity, a theory in which gravity is carried by the non-metricity scalar Q=$6H^{2}$ rather than by curvature or torsion. The working mechanism is the geometric dark-energy equation of state, which for this model takes the form ω_de(z)=−1−(2n/3)(ᴝH/$H^{2}$) and is independent of α. The authors close the underdetermined system by setting this expression equal to the CPL form ω(z)=ω_0+ω_1 z/(1+z) or the BA form ω(z)=ω_0+ω_1 z(1+z)/(1+$z^{2}$), turning the equation of state into a first-order differential equation for H(z) and producing the closed-form Hubble histories used in the MCMC fits.

What would settle it

A decisive check is to plug the best-fit values of n, ω0, and ω1 into Eqs. (18)–(20) and verify that the resulting ω_de(z) equals the CPL or BA curve that was used to close the system; a mismatch would mean the fitted H(z) is not actually a solution of the f(Q) field equations under that dark-energy parametrization.

Watch

Extended reading notes

Core claim

The paper claims that a power-law f(Q)=αQ^n model, closed by identifying the geometric dark-energy equation of state with either the CPL or BA parametrization, yields analytic H(z) solutions that fit the DESI DR2 and previous BAO Hubble data at least as well as ΛCDM. In the fits, the present-day deceleration parameter lies in −1<q(0)<0 and the present effective equation of state lies in the quintessence interval −1<ω_eff(0)<−1/3 for every dataset, with transition redshift z_tr≈0.7. The inclusion of DESI DR2 tightens the constraints and, in the DESI-only fits, drives ω_eff(z) below −1 at low redshift, suggesting a mild phantom-like late-time phase; the Om diagnostic shows a positive low-redshift slope for CPL in all datasets and dataset-dependent behavior for BA. The authors take these results to show that the model offers a competitive geometric alternative to ΛCDM for explaining late-time acceleration.

Load-bearing premise

The load-bearing assumption is that the geometric dark energy can be treated as a fluid whose pressure-to-density ratio is imposed by hand in the CPL or BA form, and that the expansion history follows from that ratio alone; this closure is an assumed ansatz, not a consequence derived from the f(Q) field equations.

Editorial extensions

If this is right

  • If the central claim is right, late-time acceleration can be produced by the non-metricity geometry of f(Q)=αQ^n without a cosmological constant, while still matching the BAO expansion history.
  • The DESI DR2 points, not just earlier BAO data, tighten the allowed ranges of H0, n, ω0, and ω1, so future BAO releases will sharpen or refute the model's predictions.
  • The transition from deceleration to acceleration at z_tr≈0.7 and the quintessence-like present-day values q(0) and ω_eff(0) are concrete predictions that can be compared against independent probes such as supernovae and cosmic chronometers.
  • Because ΔAIC and ΔBIC exceed 2 for CPL+f(Q) in most datasets, the model is statistically distinguishable from ΛCDM by these criteria, motivating a full multi-probe analysis.

Reading between the lines

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

  • Because the H(z) solutions come from prescribing the dark-energy equation of state rather than from solving the full Friedmann equation with matter and radiation, the reported constraints are constraints on the expansion history; adding CMB and supernova data, with a prior on the matter density, could remove or confirm the AIC/BIC advantage over ΛCDM.
  • The DESI-only fits push the low-redshift effective equation of state below −1, while the earlier BAO fits stay quintessence-like; this dataset sensitivity is testable, since a joint high-redshift and low-redshift analysis with the same model should pick one behavior.
  • The parameter α drops out of the geometric equation-of-state relation used to build H(z), so the fits constrain the shape exponent n and the dark-energy parameters but not the amplitude of the f(Q) correction; perturbation or structure-growth data would be needed to pin α down.
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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

4 major / 5 minor

Summary. The paper studies power-law f(Q)=αQ^n gravity combined with the CPL and BA dark-energy parametrizations. The system is closed by prescribing ω_de(z) from those parametrizations, and the resulting H(z) expressions are fit with MCMC to DESI and previous BAO H(z) data. The authors report χ²_min, AIC, BIC, and R² values that are better than or competitive with ΛCDM, and use the best-fit parameters to study q(z), ω_eff(z), and the Om diagnostic, concluding that the models yield a quintessence-like present epoch and a deceleration-to-acceleration transition, with DESI data tightening the constraints.

Significance. If the derivation and fits were correct, the paper would provide an interesting demonstration that f(Q) gravity with evolving dark-energy parametrizations is competitive with ΛCDM. The manuscript is clearly structured, uses standard statistical comparison criteria, and works with published H(z) data. However, the central derivation is internally inconsistent: Eq. (20) does not follow from Eqs. (18)-(19), and the H(z) expressions used in the likelihood omit the matter and radiation densities required by the stated Friedmann equations. As a result, the reported fit is not to the claimed f(Q)+matter cosmology, and the main conclusion is not currently supported.

major comments (4)
  1. [III, Eqs. (18)-(20)] Dividing Eq. (19) by Eq. (18) gives ω_de = -1/2 - (n/3)(\dot H/H^2), not Eq. (20), ω_de = -1 - (2n/3)(\dot H/H^2). Equation (20) also does not follow from Eq. (14) for f = αQ^n. If Eq. (20) is instead meant to follow from the conservation equation (15) together with Eq. (18), then it is inconsistent with the pressure expression (19). The derivation of the central equations (24)-(29) therefore starts from a relation that is not derived from the stated theory.
  2. [III, Eqs. (24)-(29); II, Eqs. (10)-(16)] The H(z) expressions used in the MCMC likelihood contain no matter or radiation terms. For example, Eq. (24) is a pure dark-energy expansion history, while Eq. (11) together with Eq. (16) requires ρ_m and ρ_r to enter the Friedmann equation. Consequently, the theoretical H(z) appearing in Eq. (30) is not a solution of the f(Q)+matter system introduced in Sec. II, and the χ², AIC, BIC, and R² values in Table II compare a different model to the data than the one claimed. Since q(z), ω_eff(z), and Om(z) are all derived from this H(z), the subsequent cosmological diagnostics inherit the same problem.
  3. [III, paragraph beginning 'Noting that equations...'] The authors correctly state that the system is underdetermined and then close it by prescribing the CPL or BA form for ω_de. This is an external assumption rather than a consequence of the f(Q) field equations. Moreover, because Eq. (20) then determines H(z) directly, the fitted parameters (ω0, ω1) essentially parameterize the expansion history, and the inferred n does not provide an independent constraint on the gravitational Lagrangian. The claimed 'constraint on f(Q)' is therefore circular in the present formulation.
  4. [IV, Table I and Ref. [34]] The dataset labeled 'DESI DR2 BAO' in the title and abstract is not the DESI DR2 release. Table I cites Ref. [86] (DESI 2024 VI) for the DESI H(z) points rather than the DESI DR2 paper, Ref. [34], and it lists H(z) values instead of the DR2 BAO observables (D_M/r_d, D_H/r_d, D_V/r_d) with their full covariance. The authors need to clarify which dataset was actually used; as written, the central claim about DESI DR2 is not supported by the data section.
minor comments (5)
  1. [IV, Eq. (30)] The argument list in Eq. (30) reads '(H0, n, ω0, ω0)' twice; the last argument should be ω1.
  2. [Captions of Figs. 3-5] The figure captions contain 'with redshift for for different datasets'; the duplicate 'for' should be removed. Also, 'Divison' in the affiliation is a typo.
  3. [V, Tables V and VI] Tables V and VI are announced with captions, but the actual table data do not appear in the manuscript; the best-fit values and uncertainties should be included.
  4. [References] Reference [68] currently contains the placeholder '[arXiv missing, please check]' and should be completed before submission.
  5. [IV, Table I and II] The ΛCDM comparison in Table II does not state which parameters were varied or what priors were used; this information is needed for reproducibility and for a meaningful AIC/BIC comparison.

Circularity Check

2 steps flagged · score 6.0 of 10

The fitted H(z) used in the MCMC likelihood is obtained by equating the f(Q) effective EoS to the CPL/BA ansatz and integrating, so the reported H(z), q(0), omega_eff(0), Om(z), and model-comparison statistics are consequences of the input parametrization rather than independent f(Q) predictions; Eq. (20) also does not follow from Eqs. (18)-(19).

  1. fitted input called prediction [Sec. III, after Eq. (23); Eqs. (24)-(29) and Eq. (30)]
    "Noting that equations (forρde and pde) form an underdetermined system (two equations with three unknowns:H, ρde, and pde), we close the system by prescribing a parametrization for the dark energy EoS. We consider two widely studied dark energy parametrizations schemes: the Chevallier–Polarski–Linder (CPL) and Barboza–Alcaniz (BA) parametrizations as defined by Eq. (1) and (2). Using them with Eq. (20) and (21) we obtained the two cases:"

    Equations (24) and (27) for H(z) are not obtained from the f(Q) plus matter/radiation Friedmann system (10)-(16); they are the solutions of the first-order ODE formed by setting the effective DE EoS equal to the prescribed CPL or BA function. The chi-squared function (30) then fits exactly these constructed H(z) curves through H0, n, omega0, and omega1. Consequently the reported chi2_min, AIC, BIC, R2, and the derived q(0), omega_eff(0), and Om(z) are deterministic functions of the assumed parametrization and its fitted parameters; the claim of a 'compelling geometric alternative' reduces to fitting an arbitrarily prescribed DE EoS rather than testing a first-principles f(Q) prediction.

  2. self definitional [Sec. III, Eqs. (18)-(20)]
    "ρde(z) = α·6^n(1/2−n)H^{2n}(z), pde(z) = −α·6^{n−1}(1/2−n)H^{2(n−1)}(z)(3H^2(z)+2n \dot{H}), ωde(z) = −1 − (2n/3)(\dot{H}/H^2)."

    The paper's own definitions imply ωde = pde/ρde = −1/2 − (n/3)(\dot{H}/H^2), not the −1 − (2n/3)(\dot{H}/H^2) used in Eq. (20) to close the system. Thus the H(z) formulas (24) and (27) fitted in Eq. (30) are not the EoS dictated by the f(Q) model; they are constructed from an imposed EoS with a mismatch factor. The f(Q) label is therefore attached to a curve that is defined by the input parametrization plus a fitted n, making the subsequent 'constraints' on f(Q) self-referential.

full rationale

The central derivation chain is internally consistent only in a narrow sense: once one accepts Eq. (20) and the CPL/BA closure, the H(z) expressions follow by integration. But this is not a derivation from the stated f(Q)+matter field equations. The full system (10)-(11) requires matter and radiation densities, whereas Eqs. (24) and (27) contain no Omega_m or Omega_r terms; and Eq. (20) itself contradicts the ratio of the paper's own Eqs. (18)-(19). As a result, the MCMC likelihood evaluates a different, purely parametrized expansion history, and the reported statistical preference and the values of q(0), omega_eff(0), and Om(z) are algebraic consequences of the assumed DE EoS and fitted parameters. I therefore score this as partial circularity (6), not as intentional deception: the paper explicitly labels the closure as an underdetermined-system prescription, and no load-bearing self-citation is present. The technical inconsistencies are flagged here because they make the 'f(Q) prediction' reduce to an arbitrary parametrization by construction.

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

The model introduces no new particles or fields; the free parameters are the four fitted cosmological and model parameters (H0, n, omega0, omega1) common to both parametrizations. The main ad hoc input is the imposition of the CPL/BA parametrization as a closure condition for the dark energy equation of state.

free parameters (4)
  • n = DESI: 2.45+0.64/-0.79, P-BAO: 2.40+0.89/-0.88, combined: 2.48+0.81/-0.86 for CPL; varies for BA
    Exponent in the power-law f(Q) = alpha Q^n, fitted to the BAO H(z) data in the MCMC analysis.
  • omega0 = DESI: -0.70+0.41/-0.25, P-BAO: -0.29+0.20/-0.30, combined: -0.27+0.19/-0.28 for CPL
    Present-day dark energy equation of state parameter in the CPL (and BA) parametrization, fitted to the data.
  • omega1 = DESI: 3.04+0.69/-1.06, P-BAO: 2.10+1.24/-1.11, combined: 2.26+1.11/-1.02 for CPL
    Slope parameter of the dark energy equation of state in the CPL (and BA) parametrization, fitted to the data.
  • H0 = DESI: 74.33+3.86/-4.46, P-BAO: 68.09+2.60/-3.43, combined: 68.20+2.21/-2.77 for CPL in km/s/Mpc
    Present-day Hubble constant, fitted as a free parameter in the MCMC analysis of H(z).
assumptions (4)
  • domain assumption A spatially flat FLRW universe with a curvature-free and torsion-free connection, giving Q = 6H^2.
    Invoked in Sec. II to reduce f(Q) gravity to the Friedmann equations (10)-(11).
  • domain assumption The energy-momentum tensor is a perfect fluid with separate conserved radiation, matter, and geometric dark energy components.
    Assumed in Eq. (15) to obtain the standard redshift scalings for matter and radiation densities.
  • ad hoc to paper The effective dark energy equation of state can be prescribed independently as a CPL or BA parametric form to close the underdetermined system.
    Stated explicitly in Sec. III: the system is underdetermined and is closed by prescribing a parametrization for the dark energy EoS, leading to the H(z) in Eqs. (24) and (27).
  • domain assumption The f(Q) modified Friedmann equations remain valid without extra terms arising from the connection or from a boundary term when using the power-law ansatz.
    Invoked in Sec. II when deriving the field equations and the effective dark energy density and pressure in Eq. (12).

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Cite this review

Pith. "Pith review of Constraint on Symmetric Teleparallel Gravity with Different Dark energy Parametrizations from DESI DR2 BAO Data." pith.science (2026). https://pith.science/paper/ZJ3KWIQI

@misc{pith2026250705975,
  author       = {Pith},
  title        = {Pith review of: Constraint on Symmetric Teleparallel Gravity with Different Dark energy Parametrizations from DESI DR2 BAO Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZJ3KWIQI}},
  note         = {Machine review of arXiv:2507.05975}
}
abstract

We investigate the cosmological viability of symmetric teleparallel gravity, specifically the $f(Q)$ gravity model with a power-law form $f(Q) = \alpha Q^n$, in combination with two widely used dark energy parameterizations: Chevallier Polarski Linder (CPL) and Barboza Alcaniz (BA). Employing the most recent DESI DR2 Baryon Acoustic Oscillation (BAO) dataset along with previous BAO measurements, we constrain the model parameters through a robust Markov Chain Monte Carlo (MCMC) analysis. We examine the background evolution via key cosmological indicators including the Hubble parameter $H(z)$, deceleration parameter $q(z)$, the effective equation of state $\omega_{\rm eff}(z)$, and the Om diagnostic. Our results indicate that the inclusion of DESI DR2 data significantly tightens constraints on the model parameters and supports a consistent transition from decelerated to accelerated expansion. The present-day values of $q(0)$ and $\omega_{\rm eff}(0)$ lie within the quintessence regime for all datasets. However, for lower redshift values the behaviour varies between phantom-like and quintessence-like phases. Statistical comparison via $\chi^2$, AIC, BIC, and $R^2$ further demonstrate that both CPL + $f(Q)$ and BA + $f(Q)$ provide better or competitive fits to data compared to $\Lambda$CDM, hence offering a compelling geometric alternative for explaining late-time cosmic acceleration.

Figures

Figures reproduced from arXiv: 2507.05975 by the authors.

Figure 1
Figure 1. FIG. 1. 2-d contour sub-plot for the parameters [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Plot of [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Evolution of deceleration parameter with redshift for for different datasets. The shaded regions here indicate the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Evolution of effective EoS parameter with redshift for for different datasets. The shaded regions here indicate the [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Evolution of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.