{"id":"08a92ef5-dc0a-42d4-a4b7-43c00475c461","arxiv_id":"2411.18911","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"Assumes the Lambda-CDM expansion history, labels it Barrow holographic dark energy in f(Q,C) gravity, and fits H0 and Omega0m to standard datasets.","lead":"This paper adds Barrow holographic dark energy to f(Q,C) gravity, then fits the standard Hubble parameter to supernova and cosmic clock data. The emerging dark energy behavior is largely pre-installed, because the assumed expansion history already encodes Lambda-CDM acceleration.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's central claim is unsupported because Eq. (12) imposes the ΛCDM Hubble rate by hand; the OHD/Pantheon fit tests that assumed background, not f(Q,C) gravity or Barrow entropy.","rationale":"The paper attempts to present the Barrow Holographic Dark Energy model in f(Q,C) gravity as a validated, dynamic alternative to ΛCDM, with the equation of state and other diagnostics allegedly emerging from the model and matching cosmological data. For that claim to hold, the expansion history H(z) should follow from the field equations of the theory with the assumed f(Q,C) action and BHDE energy density. Instead, the text explicitly adopts Eq. (12), the standard ΛCDM Hubble rate, without deriving it from Eqs. (6) and (7). This is the same load-bearing weakness identified by the reader: every fitted parameter and diagnostic is either forced by Eq. (12) or controlled by unconstrained internal parameters. The reported agreement with OHD and Pantheon therefore reflects the goodness of fit of ΛCDM, not the validity of the f(Q,C) or Barrow ingredients. A negative squared sound speed at z≥0, as shown in Eq. (17) and the accompanying discussion, further contradicts the claim that the model is physically stable, and the Data Availability statement directly conflicts with the reported use of 1105 data points. These are not mere presentational issues; they block the central claim that the model is a comprehensive and validated framework for cosmic acceleration. I agree with the reader's rejection and see no reason to adjust the verdict. The objection would be resolved if the authors could show that substituting the chosen f(Q,C) and ρ_BHDE into the field equations yields Eq. (12) as the unique or best-fit solution; no such derivation is provided.","tokens_in":15506,"tokens_out":3532,"duration_ms":33151,"concrete_test":"Independently derive the background evolution by substituting f(Q,C)=a1 Q^α + a2 C and ρ_BHDE = C H^(2−Δ) into the field equations (6) and (7), solving for H(z), and comparing the solution with Eq. (12). If the solution is not identically equal to Eq. (12) for the best-fit parameter values, then Eq. (12) is an external ansatz, and the reported OHD+Pantheon constraints test the ΛCDM background rather than the f(Q,C)+BHDE model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the adoption of Eq. (12), H(z)=H0[Ω0m(1+z)^3+(1−Ω0m)]^(1/2), which the text states as 'we adopt the following expression for H(z) [35]' rather than deriving it from the f(Q,C) field equations (6) and (7) together with the BHDE density (10). Because H(z) is fixed to the ΛCDM form, the subsequent quantities — the equation-of-state parameter in Eq. (16), the deceleration parameter in Eq. (21), the Om(z) diagnostic, and the statefinder pair (r,s)=(1,0) in Eq. (23) — are algebraic consequences of that assumed background, not predictions of the model. The Barrow exponent Δ, the f(Q,C) parameters α, a1, a2, and the holographic coefficient C do not enter Eq. (12), so the χ² fit to 57 OHD points and 1048 Pantheon points constrains only H0 and Ω0m; it cannot validate the Barrow entropy or f(Q,C) ingredients. The reported values H0≈70 and Ω0m≈0.262 are simply ΛCDM best-fit values. In addition, the Data Availability statement ('No data was used for the research described in the article') contradicts the reported use of OHD and Pantheon data, making the fit unreproducible as described. The central claim of a validated alternative to ΛCDM is therefore unsupported: the model is a ΛCDM background with an attached Barrow/f(Q,C) interpretation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates a Barrow Holographic Dark Energy (BHDE) model within an f(Q,C) gravity framework, using the functional form f(Q,C)=a1 Q^alpha + a2 C and the Barrow energy density rho_bhde = C H^(2-Delta). After presenting the f(Q,C) field equations for a flat FRW metric, the authors adopt a specific Hubble parameter H(z) and compute the energy density, pressure, equation-of-state parameter, squared sound speed, energy conditions, deceleration parameter, Om(z) diagnostic, and statefinder pair. They report a chi-squared fit to 57 OHD points and 1048 Pantheon points, obtaining H0 ~ 70 and Omega0m ~ 0.262, and conclude that the model transitions from matter-like behavior to dark-energy-dominated acceleration and aligns with Lambda-CDM. The central claim is that this constitutes a validated alternative description of cosmic acceleration.","tokens_in":15918,"tokens_out":4020,"duration_ms":36263,"significance":"If the model's parameters were actually constrained by the data and the background dynamics were derived from the f(Q,C) field equations, this would be a potentially interesting extension of holographic dark energy. The paper does present the field equations for f(Q,C) gravity and attempts to connect Barrow entropy with non-metricity and boundary-term gravity. However, the main significance is undercut because the adopted Hubble parameter is exactly the Lambda-CDM one, and the model-specific parameters (alpha, a1, a2, Delta, C) are never constrained. The validation reported is therefore a fit of the Lambda-CDM background, not a test of f(Q,C) gravity or Barrow entropy. The paper also contains a direct contradiction in its data availability statement, which prevents replication. Overall, the claimed comprehensive framework is not substantiated by the analysis presented.","major_comments":[{"comment":"The Hubble parameter is assumed, not derived: H(z)=H0 [Omega0m(1+z)^3 + (1-Omega0m)]^(1/2) is the Lambda-CDM expansion history, stated as 'we adopt the following expression for H(z) [35]'. It is not obtained from the field equations (6)-(7) together with the BHDE density (10) and the action (11). Because this assumed background fixes the dynamics, the subsequent equation-of-state parameter (Eq. (16)), deceleration parameter (Eq. (21)), Om(z) diagnostic, and statefinder pair (1,0) (Eq. (23)) are algebraic consequences of the input rather than predictions of the model. The Barrow parameter Delta, the action parameters a1, a2, alpha, and the holographic coefficient C do not appear in Eq. (12), so the reported chi-squared fit to OHD and Pantheon data constrains only H0 and Omega0m, reproducing the known Lambda-CDM best-fit values. This circularity invalidates the central claim of model validation.","section":"Section II, Eq. (12)"},{"comment":"The plotted curves and the reported numerical values, such as omega_BHDE(z=0) approx -0.62 and q(z=0) approx -0.60, depend on unspecified choices of the free parameters a1, a2, alpha, Delta, and C. The MCMC fit described in Section II yields only H0 and Omega0m; the paper does not report priors or best-fit values for the remaining five parameters, nor the expressions used to generate the figures. Consequently, the figures and the conclusions drawn from them are not reproducible from the information given.","section":"Sections III.3 and IV, Figures 2-8"},{"comment":"The squared sound speed in Eq. (17) is negative for z >= 0, as the text explicitly states ('potential instability in the BHDE model during the high-redshift phase' and 'remains negative' at z=0). Yet the concluding section claims that 'the model effectively resolves initial perturbations, ensuring long-term stability.' A negative pressure-gradient speed is a known instability for dark energy perturbations unless a specific physical mechanism or a full perturbative analysis is provided; none is supplied here. The statement in the conclusion is therefore unsupported and inconsistent with the stability analysis presented in Section III.4.","section":"Section III.4, Eq. (17) and Section V"},{"comment":"The Data Availability statement reads 'No data was used for the research described in the article,' which directly contradicts the detailed description in Section II of using 57 OHD data points (0 <= z <= 2.36) and 1048 Pantheon SN Ia data points and performing a chi-squared minimization. This contradiction makes the reported constraints and figures unreproducible and calls into question the provenance of the observational results.","section":"Data Availability statement and Section II"}],"minor_comments":[{"comment":"All figure captions in Section III and IV say 'The behavior of statefinder parameters of the fluid,' but the panels show energy density, pressure, equation of state, sound speed, energy conditions, deceleration parameter, and Om(z); the captions should be corrected to match each plotted quantity.","section":"Figures 2-8"},{"comment":"Equation (15) uses the symbol gamma in the pressure expression while Equation (16) uses alpha for what appears to be the same exponent; the notation should be made consistent, or the relationship between gamma and alpha should be defined.","section":"Equations (15)-(16)"},{"comment":"The text says 'By solving equations (20) and (21), we derived the equation of state parameter' but there are no numbered equations (20) and (21) at that point; the reference should be to the preceding energy density and pressure equations, such as (14) and (15).","section":"Section III.3, derivation of omega"},{"comment":"The abstract claims predictions 'align well with observational datasets, including Type Ia supernovae, cosmic microwave background (CMB) radiation, and baryon acoustic oscillations (BAO),' but the analysis in Section II only uses OHD and Pantheon data; the CMB and BAO claims are not supported by any analysis in the manuscript.","section":"Abstract and Section II"},{"comment":"The paper defines Om(z) = [E(z)]^2 - 1, omitting the denominator (1+z)^3 - 1 that appears in the standard Om diagnostic introduced by Sahni et al. (2008). As a result, the 'model-independence' attributed to Om(z) is inaccurate, and the interpretation of the plotted Om(z) behavior should be revisited.","section":"Section IV.2, Om(z) definition"}],"recommendation":"reject","confidential_remarks":"The central issue is not a disagreement with the consensus but an internal circularity: the assumed Hubble parameter in Eq. (12) is exactly Lambda-CDM, so the comparison with OHD and Pantheon data cannot validate the Barrow holographic or f(Q,C) ingredients. The additional data-availability contradiction and the lack of reported parameter choices for the figures make the paper unsuitable for publication in its current form. A complete reworking, in which the background is derived from the field equations and the model parameters are genuinely constrained, would be needed before this manuscript could be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things up front. First, this is not an independent test of Barrow entropy or f(Q,C) gravity: the Hubble parameter in Eq. (12) is the ΛCDM expansion history, adopted by hand with a citation to the authors' own earlier paper. Second, the paper does have a usable core—the field equations for f(Q,C) are written down correctly, and the algebra from those equations to the EoS, deceleration parameter, statefinder, and energy conditions is internally consistent, as far as I checked. That is real work, and the presentation is readable. But the central claim in the abstract and conclusion—that the model provides a validated alternative to ΛCDM—is not supported. Because H(z) is fixed by hand, the derived ω(z), q(z), and statefinder (1,0) are algebraic consequences of ΛCDM, not predictions of the Barrow or f(Q,C) ingredients. The parameters Δ, α, a1, a2, C never enter Eq. (12), so the χ² fit to OHD and Pantheon constrains only H0 and Ω0m, and the reported values (H0≈70, Ω0m≈0.262) are just the standard ΛCDM best fit. That is the soft spot, and it is load-bearing. There are also smaller problems. The squared sound speed is negative for z≥0, which the text admits; claiming this 'aligns' with Bellini, Alam, and DES is a stretch, since those works do not validate negative sound speeds in this setup. The Data Availability statement says no data were used, which directly contradicts the fitted OHD and Pantheon samples, making the fit unreproducible as described. The text also has errors (e.g., the EoS reference to 'equations (20) and (21)' when the relevant equations are (14) and (15), and the section header that mentions f(Q,T)). None of these are fatal to the algebra, but they add noise. The citation pattern is conventional and mostly relevant; self-citation to ref. [35] is legitimate here because the construction is indeed a transplant, which only reinforces the novelty concern. Who is this for? Someone cataloging f(Q,C) phenomenology might want it on record, and a referee could usefully force the authors to state clearly that their fit does not distinguish the model from ΛCDM. But it is not a serious competitor to ΛCDM and it does not deliver the validation the abstract promises. My recommendation: if you have to referee it, accept the assignment but mark it as a modest phenomenological exercise needing major revision; if you are deciding whether to engage on your own, skip it unless you work on f(Q,C) model classification.","headline":"A routine transplant of the authors' f(Q,T) BHDE work into f(Q,C) gravity, where the assumed ΛCDM Hubble parameter does all the work and the new ingredients are never constrained.","tokens_in":16416,"tokens_out":677,"would_cite":false,"duration_ms":8171,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83F05","83D05"],"pacs":["98.80.-k","04.50.Kd","95.36.+x"],"model":"deepseek-v4-flash","headline":"This paper claims that a Barrow holographic dark energy model in f(Q,C) gravity can reproduce the observed cosmic acceleration, with an equation of state that evolves from matter-like values in the past to -1 in the future.","keywords":["Barrow Holographic Dark Energy","f(Q,C) gravity","non-metricity","cosmic acceleration","equation of state","Lambda-CDM","Pantheon supernovae","Hubble parameter"],"falsifier":"Compute the linear growth index from the f(Q,C) perturbation equations for the best-fit parameters; if the predicted f sigma_8(z) at z=0.5 disagrees with the combined Planck, BAO, and redshift-space-distortion measurements by more than the reported error, the model is ruled out despite its background fit.","tokens_in":15316,"feed_emoji":"🌌","tokens_out":7355,"duration_ms":61832,"temperature":0.7,"pith_summary":"This paper aims to show that Barrow Holographic Dark Energy in f(Q,C) gravity, a modified theory built from the non-metricity scalar Q and its boundary term C, can account for the late-time acceleration of the universe without a cosmological constant. The authors adopt the standard Lambda-CDM expansion history H(z)=H0[Omega0m(1+z)^3+(1-Omega0m)]^{1/2}, add the Barrow entropy-corrected holographic energy density rho_bhde = C H^{2-$\\Delta$}, and derive the pressure from the f(Q,C)=a1 Q^$\\alpha$ + a2 C action. They then fit H0 and Omega0m to 57 OHD data points and the Pantheon SNe Ia sample, obtaining H0=70.01 and Omega0m=0.262, and find the equation of state goes from matter-like values at high redshift to -0.62 today and asymptotically to -1 at z=-1. The point of the paper is that this dynamic, quantum-gravity-inspired dark energy reproduces the same background diagnostics as Lambda-CDM while offering a geometric explanation.","feed_headline":"Barrow dark energy curve ends at -1, matching Lambda-CDM","feed_subtitle":"An f(Q,C) gravity fit to OHD and Pantheon gives EoS about -0.62 today and a Lambda-CDM background.","key_machinery":"The central machinery is the ansatz H(z)=H0 $\\sqrt$(Omega0m(1+z)^3 + (1-Omega0m)), equation (12), which fixes the expansion history to exactly Lambda-CDM, combined with the Barrow holographic energy density rho_bhde=C H^{2-$\\Delta$}, where $\\Delta$ measures the fractal deformation of the black-hole horizon. Feeding these into the f(Q,C) field equations with f(Q,C)=a1 Q^$\\alpha$ + a2 C generates closed-form expressions for pressure, equation of state, sound speed, and energy conditions, so that every diagnostic plotted is an algebraic consequence of the assumed H(z), the Barrow density, and the chosen f(Q,C) form.","core_discovery":"On the paper's own terms, the discovery is that coupling Barrow's fractal black-hole entropy to the f(Q,C) gravitational action yields a holographic dark energy whose equation of state is dynamically evolving yet asymptotically Lambda-CDM. Specifically, with the Hubble rate fixed to the Lambda-CDM form, the derived EoS parameter omega_bhde is near zero at z>0, equals about -0.62 at the present epoch, and converges to -1 as z approaches -1, while the deceleration parameter switches from positive to negative at z about 0.74 and the statefinder pair is (r,s)=(1,0). The null and dominant energy conditions hold throughout, while the strong energy condition is violated at late times, matching the standard picture of acceleration. The authors read this as evidence that the BHDE model inside f(Q,C) gravity is a viable dynamical alternative to a static cosmological constant.","pith_inferences":["The authors do not claim, but it follows from their setup, that because Eq. (12) is assumed rather than derived, the kinematical diagnostics (q, Om(z), statefinder) cannot distinguish f(Q,C) gravity from Lambda-CDM.","A testable extension the paper leaves implicit would be to derive H(z) from the f(Q,C) field equations with rho_bhde as the matter source, rather than inputting the Lambda-CDM expansion by hand.","Another extension: compute the growth rate f sigma_8 from linear perturbations of this action; since perturbation dynamics depend on the full f(Q,C) structure, that observable would test the model beyond its background fit.","The Barrow exponent Delta in rho_bhde just rescales the density as H^{2-Delta}; an independent constraint on Delta (for example, from black-hole thermodynamics or a joint background-plus-perturbation fit) would separate the Barrow contribution from the f(Q,C) parameters."],"forward_implications":["The EoS parameter evolves from matter-like values near zero at z>0 to -0.62 today and to -1 at z=-1, so the model behaves like a dynamical dark energy that settles into a cosmological-constant phase in the far future.","The deceleration parameter crosses zero at z approximately 0.74, giving the observed transition from deceleration to acceleration without invoking a cosmological constant.","The statefinder pair (r,s)=(1,0) matches Lambda-CDM, so on the background geometry the model is indistinguishable from Lambda-CDM.","The null and dominant energy conditions hold at all redshifts while the strong energy condition is violated at z<=0, consistent with a repulsive late-time acceleration.","The sound-speed parameter is negative for z>0 and approaches zero at z=-1, indicating transient instabilities that fade in the distant future."],"supporting_citations":[{"why":"Supplies the modified Barrow entropy law S=(A/A0)^{1+Delta/2} that defines the fractal horizon and leads to the BHDE density.","marker":"[30]"},{"why":"Establishes the f(Q,C) gravitational action and field equations used to derive pressure and energy conditions.","marker":"[20]"},{"why":"Provides the holographic dark energy bound rho_DE L^4 <= S from which rho_bhde = C L^{Delta-2} is obtained.","marker":"[31]"},{"why":"The adopted Hubble parameter H(z)=H0[...]^{1/2} is taken from this earlier Barrow holographic dark energy work; it fixes the Lambda-CDM background used throughout.","marker":"[35]"},{"why":"Planck 2018 results are used as the external consistency check for the fitted equation-of-state values.","marker":"[41]"}],"fun_headline_variants":["Barrow dark energy in f(Q,C) gravity tracks Lambda-CDM","EoS hits -0.62 today, then -1: Barrow model matches Lambda-CDM","Dark energy from Barrow entropy asymptotes to -1 in f(Q,C) gravity","Deceleration flips at z=0.74 in Barrow f(Q,C) model","Barrow holographic model in f(Q,C) gravity: EoS evolves to -1"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the expansion history is already known to be Lambda-CDM: equation (12) fixes H(z) by hand, and all subsequent parameters, including the equation of state, deceleration parameter, and statefinder pair, are derived from that choice rather than from the f(Q,C) dynamics.","fun_headline_variants_meta":{"raw":{"variants":["Barrow dark energy in f(Q,C) gravity tracks Lambda-CDM","EoS hits -0.62 today, then -1: Barrow model matches Lambda-CDM","Dark energy from Barrow entropy asymptotes to -1 in f(Q,C) gravity","Deceleration flips at z=0.74 in Barrow f(Q,C) model","Barrow holographic model in f(Q,C) gravity: EoS evolves to -1"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000892,"raw_usage":{"total_tokens":3866,"prompt_tokens":985,"completion_tokens":2881,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":2768}},"tokens_in":601,"tokens_out":2881,"duration_ms":17532,"temperature":1.0,"reasoning_tokens":2768,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T10:44:30.372360+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the linear growth index from the f(Q,C) perturbation equations for the best-fit parameters; if the predicted f sigma_8(z) at z=0.5 disagrees with the combined Planck, BAO, and redshift-space-distortion measurements by more than the reported error, the model is ruled out despite its background fit.","supporting_citations":[{"cited_title":"Freese and M","cited_arxiv_id":null,"evidence_quote":"Establishes the f(Q,C) gravitational action and field equations used to derive pressure and energy conditions."},{"cited_title":"Samaddar, S","cited_arxiv_id":null,"evidence_quote":"Provides the holographic dark energy bound rho_DE L^4 <= S from which rho_bhde = C L^{Delta-2} is obtained."}],"review_version":1}