{"id":"6ef051a1-71a9-420d-b8a6-f982f81a5589","arxiv_id":"2507.05975","paper_version":1,"verdict":"REJECT","confidence":"LOW","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"MCMC fits of CPL and BA dark energy parametrizations in power-law f(Q) gravity to DESI DR2 and prior BAO H(z) data find statistically competitive or better fits than Lambda-CDM.","lead":"The paper fits a power-law f(Q) gravity model with two dark energy parametrizations (CPL and BA) to DESI DR2 and older BAO Hubble data, and reports that both models fit the data better than Lambda-CDM. The authors claim the models describe the cosmic deceleration-to-acceleration transition while staying in the quintessence regime today.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fitted H(z) is not a solution of the stated f(Q)+matter system: Eq. (20) contradicts Eqs. (18)-(19), and Eqs. (24)/(27) omit the matter/radiation density terms required by Eqs. (10)-(11).","rationale":"The most load-bearing condition for the paper's central claim is that Eqs. (24)-(29) are genuine background solutions of the f(Q)+matter system. They are not: Eq. (20) does not follow from the printed definitions in Eqs. (18)-(19), and the integrated H(z) contains no matter or radiation density term even though Eqs. (10)-(11) and (15)-(16) explicitly include those components. The MCMC therefore fits a pure dark-energy ansatz rather than the stated f(Q)+CPL/BA cosmology, making the reported statistical comparisons with Lambda-CDM uninterpretable as evidence for f(Q) gravity. The reader's concern about closing the system by prescribing omega_de is related, but the concrete algebraic and dynamical inconsistency is more fundamental. An independent re-derivation and a full re-fit including Omega_m0 would settle the issue. Since this concern reinforces rather than changes the reader's rejection, the verdict remains unchanged.","tokens_in":16792,"tokens_out":12254,"duration_ms":130201,"concrete_test":"Independently re-derive the background: (1) compute p_de/rho_de from the printed Eqs. (18)-(19) and compare with Eq. (20); (2) solve the full Friedmann equation (10) together with rho_m = rho_m0(1+z)^3, rho_r = rho_r0(1+z)^4, and the CPL condition on omega_de, treating Omega_m0 and alpha as parameters. If the resulting H(z) differs from Eq. (24), re-run the DESI/P-BAO likelihood with the corrected H(z); the claim of a better fit than Lambda-CDM must be re-evaluated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central statistical claim rests on the H(z) expressions (24)-(29), but those expressions do not follow from the stated f(Q) system. In the CPL case, Eq. (20) is equated with the CPL form to solve for H(z); however, Eq. (20) is not derivable from the preceding definitions: taking omega_de = p_de/rho_de from Eqs. (18)-(19) gives -1/2 - (n/3) Hdot/H^2, not -1 - (2n/3) Hdot/H^2. More importantly, the resulting H(z) contains no matter or radiation term: Eq. (24) is a pure dark-energy solution with no Omega_m or Omega_r, even though Eqs. (10)-(11) and (15)-(16) require rho_m = rho_m0(1+z)^3 and rho_r = rho_r0(1+z)^4 in the Friedmann equation. The MCMC likelihood (30) therefore evaluates a different model than the claimed f(Q)+CPL/BA cosmology, so the reported chi^2_min, AIC, BIC, and R^2 comparisons do not support the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16933,"tokens_out":11696,"duration_ms":119551,"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":[{"comment":"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.","section":"III, Eqs. (18)-(20)"},{"comment":"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.","section":"III, Eqs. (24)-(29); II, Eqs. (10)-(16)"},{"comment":"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.","section":"III, paragraph beginning 'Noting that equations...'"},{"comment":"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.","section":"IV, Table I and Ref. [34]"}],"minor_comments":[{"comment":"The argument list in Eq. (30) reads '(H0, n, ω0, ω0)' twice; the last argument should be ω1.","section":"IV, Eq. (30)"},{"comment":"The figure captions contain 'with redshift for for different datasets'; the duplicate 'for' should be removed. Also, 'Divison' in the affiliation is a typo.","section":"Captions of Figs. 3-5"},{"comment":"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.","section":"V, Tables V and VI"},{"comment":"Reference [68] currently contains the placeholder '[arXiv missing, please check]' and should be completed before submission.","section":"References"},{"comment":"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.","section":"IV, Table I and II"}],"recommendation":"reject","confidential_remarks":"The core derivation of the model that is actually fitted is internally inconsistent, so the central claim cannot be supported without replacing the model and redoing the full analysis. I also recommend verifying the data provenance, since the manuscript appears to use DESI 2024 H(z) values rather than the DESI DR2 BAO release cited in the title."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take on arXiv:2507.05975. It's a straightforward MCMC fitting of power-law f(Q)=αQ^n with CPL and BA dark energy EoS parametrizations to DESI DR2 BAO H(z) data, comparing to ΛCDM via χ², AIC, BIC, R². That's a common exercise in the f(Q) subfield, and the data analysis is transparent. The authors also honestly note they only use a limited part of DESI DR2.\n\nThe problem is that the theory section doesn't hang together. Their Eq. (20) for ω_de doesn't follow from Eqs. (18)–(19); working from those definitions gives ω_de = -1/2 - (n/3) Hdot/H², not -1 - (2n/3) Hdot/H². That's a factor of two in both terms. More importantly, the H(z) solutions in (24) and (27) contain no matter or radiation density terms at all. The field equations they wrote (10)–(11) include ρ_m ∝ (1+z)³ and ρ_r ∝ (1+z)⁴, so the actual H(z) for the f(Q)+matter system should depend on Ω_m and Ω_r. Their fitted H(z) doesn't, and they never introduce those parameters. The likelihood (30) is therefore evaluating a different model—a pure dark-energy universe—not the f(Q)+matter cosmology they claim to constrain.\n\nThat kills the central statistical claim. Comparing a no-matter model against ΛCDM (which includes matter) and declaring, on that basis, that f(Q)+CPL is a \"compelling geometric alternative\" isn't justified. The AIC/BIC numbers themselves are internally consistent (for N=5, 27, 32), despite what the reader's report says; the problem is the model being scored.\n\nOn the data handling: they fit H(z) values with diagonal errors rather than the DESI BAO distance likelihood with its covariance, and they combine P-BAO with DESI without accounting for correlations. That's a softer issue and common in this literature, but it compounds the main problem.\n\nWho is this paper for? People who want to see yet another f(Q) model constrained by DESI DR2, with the usual q(z), ω_eff(z), Om plots. The plots and tables are fine. But as it stands, the derivation error and the missing matter/radiation term mean the results don't bear on whether power-law f(Q) fits the data.\n\nMy recommendation: don't cite it in its current form, and if you review it, reject with the option to resubmit after correcting the Friedmann equations and refitting with Ω_m. It does deserve a serious referee rather than a desk reject, because the data work is real and the fix is tractable, but the current version's conclusion is unsupported.","headline":"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.","tokens_in":17600,"tokens_out":10641,"would_cite":false,"duration_ms":96747,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83F05"],"pacs":["98.80.-k","04.50.Kd","95.36.+x"],"model":"deepseek-v4-flash","headline":"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.","keywords":["f(Q) gravity","symmetric teleparallel gravity","dark energy parametrization","CPL parametrization","BA parametrization","DESI DR2 BAO","MCMC parameter constraints","late-time cosmic acceleration"],"falsifier":"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.","tokens_in":16467,"feed_emoji":"🌌","tokens_out":11089,"duration_ms":117150,"temperature":0.7,"pith_summary":"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.","feed_headline":"Power-law f(Q) gravity clears DESI DR2 BAO tests","feed_subtitle":"With CPL or BA dark energy, its expansion-history fits match or beat ΛCDM on AIC and BIC.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines f(Q) symmetric teleparallel gravity and the non-metricity formalism that produces the geometric dark-energy sector.","marker":"[15, 16]"},{"why":"Earlier claim that f(Q) gravity can outperform ΛCDM, the result this paper extends to evolving dark-energy parametrizations.","marker":"[17]"},{"why":"Provides the CPL equation-of-state parametrization used to close the model.","marker":"[30, 31]"},{"why":"Provides the BA equation-of-state parametrization used as the second closure.","marker":"[33]"},{"why":"Supplies the DESI DR2 BAO data whose inclusion tightens the parameter constraints.","marker":"[34]"},{"why":"Supplies the DESI 2024 BAO Hubble points used as the previous-BAO dataset and comparison.","marker":"[86]"}],"fun_headline_variants":["f(Q) gravity with CPL/BA matches DESI DR2 BAO fits","Power-law f(Q) model rivals ΛCDM on DESI BAO data","DESI DR2 data tightens f(Q) gravity constraints","Geometric dark energy from f(Q) passes BAO tests","f(Q) model with CPL dark energy fits DESI BAO well"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["f(Q) gravity with CPL/BA matches DESI DR2 BAO fits","Power-law f(Q) model rivals ΛCDM on DESI BAO data","DESI DR2 data tightens f(Q) gravity constraints","Geometric dark energy from f(Q) passes BAO tests","f(Q) model with CPL dark energy fits DESI BAO well"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000539,"raw_usage":{"total_tokens":2633,"prompt_tokens":1043,"completion_tokens":1590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":659,"completion_tokens_details":{"reasoning_tokens":1492}},"tokens_in":659,"tokens_out":1590,"duration_ms":10979,"temperature":1.0,"reasoning_tokens":1492,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:12:55.317629+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"M., & Alcaniz, J","cited_arxiv_id":null,"evidence_quote":"Provides the BA equation-of-state parametrization used as the second closure."}],"review_version":1}