{"id":"83e3e9ce-355b-44c1-8cf2-d24c77be3e95","arxiv_id":"2505.21359","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Nonflat teleparallel dark energy with a vanishing potential is statistically favored over Lambda CDM in the authors' MCMC fit and mildly prefers an open universe.","lead":"A study tests a teleparallel model of dark energy in a universe whose space is curved, using supernovae, cosmic chronometers, and galaxy growth data. It reports that a model with no scalar potential is strongly preferred over the standard dark energy cosmology and better matches nearby measurements of cosmic expansion.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Growth-rate claims and the V=0 model preference rely on a flat-space quasi-static Geff that is asserted, not derived, for curved FLRW, and the paper itself concedes the linear perturbation sector may be incomplete; the headline ΔAIC/DIC result is therefore conditional.","rationale":"The reader's weakest-assumption analysis identifies exactly the same load-bearing point: the growth-sector phenomenology is built on a flat-space quasi-static Geff whose validity in a curved FLRW background is asserted rather than demonstrated. I read the paper in good faith and find the background dynamics, the autonomous system, and the MCMC implementation internally consistent as far as they go; the tension-alleviation and model-selection claims follow from the stated pipeline. The decisive weakness is that the pipeline's growth part depends on Geff from Eq. (26), and the final remark itself flags a known strong-coupling caveat for teleparallel cosmological perturbations. Because GRF data enter the joint likelihood used for parameter estimation and model comparison, this unresolved caveat makes the ΔAIC/ΔDIC result conditional rather than decisive. I therefore keep the reader's CONDITIONAL verdict unchanged. As a secondary note, Eq. (35a) does not match the V=0 limit of the general system (30a): the factor (x5^2 − 2) is missing, which would change the sign of the ξ term in the flat limit. Since Section IV states that the numerical integration uses system (30), I do not make this typographical discrepancy the primary objection, but it should be corrected in a revision.","tokens_in":16818,"tokens_out":14220,"duration_ms":157614,"concrete_test":"Derive the full linear scalar perturbation equations for action (11) around the nonflat FLRW tetrad (14), keeping all curvature-dependent terms in the subhorizon quasi-static limit, and extract the effective Poisson equation. Compare the resulting Geff with Eq. (26); if corrections involving ξΩk or (k/aH)^2 appear at redshifts covered by the 18 GRF data points, rerun the joint MCMC with the corrected Geff and check whether S8 and the Table II ΔAIC/ΔDIC values shift by more than the quoted uncertainties. If the corrected Geff agrees with Eq. (26) to the relevant precision, the central claim stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing premise is that the effective gravitational coupling Geff in Eq. (26), obtained from flat-space quasi-static linear perturbation theory, continues to hold on a spatially curved FLRW background. Section II B asserts this holds when the curvature scale is much larger than the perturbation scale, but no derivation or quantitative criterion is supplied. The same Geff enters the growth equation (43) via Eq. (33), so the reported S8 values and the GRF contribution to the joint likelihood — and hence the ΔAIC = −10.4 and ΔDIC = −14.1 preference for the V=0 model in Table II — are conditional on this unverified extension. The final remark explicitly concedes that linear perturbation analyses around highly symmetric FLRW backgrounds may not reveal all dynamical degrees of freedom suggested by Hamiltonian analyses of teleparallel gravity; if such degrees of freedom couple to matter, the growth equation used here is incomplete. This is not an internal inconsistency in the MCMC pipeline, but an unresolved physical assumption that the paper's strongest statistical claim does not survive without.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends teleparallel dark energy (TDE) with a nonminimally coupled scalar field to a spatially curved FLRW background. The authors build a dynamical-system formulation for three potentials (zero, exponential, power-law), then run an MCMC analysis on the joint Pantheon+SH0ES+CC+GRF likelihood. They report that the zero-potential nonflat TDE model is very strongly preferred over ΛCDM (ΔAIC=-10.4, ΔDIC=-14.1), that all TDE models yield h≈0.717 and S8≈0.77-0.80, and that these values are closer to local H0 and low-redshift growth measurements than Planck-ΛCDM predictions.","tokens_in":16991,"tokens_out":5837,"duration_ms":65066,"significance":"If the central claim holds, the paper demonstrates that a minimal torsion-scalar action with spatial curvature can simultaneously move H0 toward the local distance-ladder value, lower S8 relative to Planck, and statistically outperform ΛCDM on the chosen data combination. The dynamical-system construction is transparent, the MCMC pipeline is internally consistent, and the paper provides clear tables of best-fit values and information criteria. The significance is nonetheless conditional: the growth-rate sector relies on a flat-space quasi-static effective gravitational coupling that is asserted rather than derived for curved FLRW, and the reported H0 compatibility is partly circular because the SH0ES calibration is inside the fitted likelihood.","major_comments":[{"comment":"The effective gravitational coupling Geff in Eq. (26) is imported from flat-space quasi-static linear perturbation theory and used in the nonflat growth equation (43) without a derivation. The manuscript asserts that the expression holds when the curvature scale is much larger than the perturbation scale, but it provides no quantitative criterion or check against the posterior values of Ωk,0. Because the GRF data enter the joint likelihood and thus the reported ΔAIC and ΔDIC in Table II, the headline preference for the V=0 model is conditional on this unverified extension. The final remark in Sec. V concedes that linear perturbation analyses around FLRW may be incomplete in teleparallel gravity, which further underscores the need to either derive Geff for nonflat backgrounds or demonstrate explicitly that curvature corrections are negligible at the scales probed by the growth data.","section":"Sec. II.B, Eq. (26); Sec. IV, Eq. (43)"},{"comment":"The prior on ξ is restricted to the interval [-1,0], so the posterior means ξ≈-0.34 lie in the middle of the allowed range and the statement that the coupling is \"robustly constrained to negative values\" is a restatement of the prior support. Because ξ=0 is excluded a priori, the data cannot discriminate between a minimal coupling and the negative values reported. To support the claim of a significant nonminimal coupling, the analysis should be repeated with a prior that includes ξ=0 (e.g., [-1,1]) or with a model-comparison statistic that properly accounts for the prior volume.","section":"Sec. IV.A, Table I and prior on ξ"},{"comment":"The agreement between the fitted h≈0.717 and the SH0ES local value is not an independent confirmation of the model: h is a free parameter and the SH0ES Cepheid host distances are part of the Pantheon+SH0ES likelihood used in Eq. (45). The reported value is therefore a fit to, not a prediction of, the local distance ladder. The interpretation that the model alleviates the H0 tension should be reframed as consistency with the SH0ES calibration included in the data, rather than as a resolution of the tension.","section":"Sec. IV.B and Sec. V (H0 compatibility)"}],"minor_comments":[{"comment":"The abstract refers to \"Bayesian information criteria,\" but the paper computes the Akaike information criterion (AIC) and the deviance information criterion (DIC); the Bayesian information criterion (BIC) is not used. The wording should be changed to \"information criteria\" or the specific criteria should be named.","section":"Abstract"},{"comment":"There is a typo \"FRLW\" in the concluding section; it should be \"FLRW.\"","section":"Sec. V"},{"comment":"The phrase \"the the null potential\" contains a duplicated article and should be corrected.","section":"Sec. IV.A"},{"comment":"For the V=0 model, σ8 has a 1σ uncertainty of ±0.118, yielding S8=0.801±0.150, which is consistent with the Planck value 0.832±0.013 at about 1σ. The statement that the model is in better agreement with low-redshift growth data should be tempered by this large uncertainty, since the difference is not statistically significant.","section":"Table I and Sec. IV.B"}],"recommendation":"major_revision","confidential_remarks":"The paper's core statistical analysis is internally coherent, but the strength of the conclusions is overstated in three respects that I have raised as major comments: the unverified flat-space Geff in the growth sector, the sign-restricted prior on ξ, and the circularity of the H0 comparison. The referee report should make clear that the headline ΔAIC/ΔDIC result is conditional on the Geff assumption. The authors may be able to address these points with additional checks and revised interpretation, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThis paper does what it says: it extends the flat teleparallel dark energy analysis of [56] to non-flat FLRW, introduces a curvature variable x5 and k-dependent corrections to the effective dark energy density and pressure, and runs a clean MCMC pipeline against Pantheon+SH0ES, cosmic chronometers, and growth-rate data. The background sector is legible and the dynamical system is competently handled. The authors are honest about the main caveat: the final remark concedes that linear perturbation theory around FLRW may miss dynamical degrees of freedom in teleparallel gravity.\n\nThe soft spot is load-bearing. Equation (26), the effective gravitational coupling Geff, was derived for flat space under the quasi-static approximation. The paper asserts it remains valid for curved FLRW when the curvature scale is much larger than the perturbation scale, but no derivation or quantitative criterion is given. That Geff enters the growth equation (43), so the reported S8 values and the strong statistical preference for the V=0 model (Delta AIC = -10.4, Delta DIC = -14.1) all inherit this assumption. The authors themselves flag that strong coupling may make the linear perturbation analysis incomplete, which means the headline result is conditional on a physically unresolved issue. I do not see an internal inconsistency in the MCMC pipeline, but the growth sector needs a much tighter derivation before those numbers should be quoted as a victory over Lambda CDM.\n\nA smaller soft spot: h is a fitted parameter and the SH0ES Cepheid distances are inside the Pantheon+SH0ES likelihood, so the agreement with the local H0 is not an independent confirmation. The comparison with Planck is still informative, but the 'compatible with local determinations' language oversells what is actually tested. Minor: convergence diagnostics and chain details are not shown, though the posterior plots look reasonable.\n\nWho gets value from this? Cosmologists working on modified gravity and the H0/S8 tensions. The background constraints and the negative xi coupling are useful, and the extension to non-flat geometry is a legitimate contribution. With the growth-sector caveat, the paper deserves a serious referee. I would send it to review and ask the authors to either derive the curved-space Geff or clearly downgrade the growth and model-selection claims to conditional.","headline":"A clean, honest extension of teleparallel dark energy to non-flat FLRW, whose headline preference over Lambda CDM rests on an asserted rather than derived curved-space Geff and on a growth sector the authors themselves flag as incomplete.","tokens_in":17562,"tokens_out":3270,"would_cite":false,"duration_ms":34141,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83F05","83B05"],"pacs":["04.50.Kd","95.36.+x","98.80.-k"],"model":"deepseek-v4-flash","headline":"Teleparallel dark energy with a vanishing scalar potential is decisively preferred over the standard cosmological model in a combined fit of supernovae, chronometers, and growth data.","keywords":["teleparallel gravity","dark energy","nonminimal scalar-torsion coupling","spatial curvature","Hubble tension","S8 tension","Markov chain Monte Carlo","dynamical systems"],"falsifier":"Deriving the full linear scalar perturbations in covariant teleparallel gravity on a nonflat FLRW background would settle the matter: if the Poisson equation acquires a correction of order $k/(a^2H^2)$ relative to Eq. (26), the reported $S_8$ and $\\Delta\\mathrm{AIC}$ values would shift; alternatively, re-running the MCMC without the growth-rate data tests whether the decisive $\\Delta\\mathrm{AIC}=-10.4$ preference survives without the assumed $G_{\\mathrm{eff}}$.","tokens_in":16499,"feed_emoji":"🌌","tokens_out":11082,"duration_ms":126066,"temperature":0.7,"pith_summary":"The paper tries to establish that teleparallel dark energy, a scalar field nonminimally coupled to torsion rather than to curvature, remains viable once spatial curvature is included, and that its simplest version with a zero scalar potential is statistically preferred over the standard $\\Lambda$CDM model. Fitting Pantheon+SH0ES supernovae, cosmic chronometers, and growth-rate data jointly, the authors find $\\Delta\\mathrm{AIC} = -10.4$ and $\\Delta\\mathrm{DIC} = -14.1$ for the vanishing-potential nonflat scenario, a margin conventionally read as decisive. All three potential choices give $h \\approx 0.717$, matching local SH0ES measurements, and $S_8 \\approx 0.77\\text{--}0.80$, lower than the Planck value and closer to low-redshift structure probes. The posterior distributions mildly favor an open geometry, with positive $\\Omega_{k,0}$, while remaining consistent with a flat universe at the $1\\sigma$ level.","feed_headline":"Teleparallel dark energy beats ΛCDM by 10 AIC points","feed_subtitle":"A scalar field coupled to spatial torsion pulls the Hubble constant toward local readings and eases the growth tension.","key_machinery":"The load-bearing object is the nonminimal scalar-torsion coupling $\\xi T\\phi^2$ inside the action. For the diagonal tetrad on FLRW, the torsion scalar is $T = -6\\left(H^2 - k/a^2\\right)$, so the same coupling enters the background and the perturbation equations. The scalar field acts as an effective dark-energy fluid with density and pressure given by Eqs. (20)–(21), and its equation of state $w_{\\mathrm{DE}}$ can cross the phantom divide. The growth sector is governed by Eq. (43) with the effective gravitational coupling $$\\frac{G_{\\mathrm{eff}}}{G} = \\frac{1 - $3x_1^{2}$ + \\xi $x_4^{2}$}{(1 + \\xi $x_4^{2}$)^2},$$ where $x_1$ and $x_4$ are dynamical-system variables related to the scalar kinetic term and the field value. Because $\\xi$ is constrained to negative values around $-0.34$, this $G_{\\mathrm{eff}}$ differs from Newton's constant and suppresses the growth of matter fluctuations, which is what makes $S_8$ come out low. Curvature enters through the dynamical variable $x_5 = \\sqrt{1 + k/(a^2H^2)}$, and the autonomous system of dimensionless variables converts the field equations into a form suitable for Markov chain Monte Carlo sampling.","core_discovery":"The central claim is that in a Friedmann-Lemaître-Robertson-Walker universe with arbitrary spatial curvature $k$, the teleparallel dark energy action $$S = \\int $d^{4}$x\\, e\\left[\\frac{T}{2\\$kappa^{2}$} + \\frac{1}{2}\\partial_\\mu\\phi\\,\\partial^\\mu\\phi + \\xi T\\$phi^{2}$ - V(\\phi) + \\mathcal{L}_m\\right]$$ produces an effective dark-energy fluid that fits the combined Pantheon+SH0ES+CC+GRF data better than $\\Lambda$CDM, with the vanishing potential $V(\\phi)=0$ as the standout case: $\\Delta\\mathrm{AIC}=-10.4$ and $\\Delta\\mathrm{DIC}=-14.1$ relative to $\\Lambda$CDM, while exponential and power-law potentials remain statistically comparable. The fit for $V=0$ yields $h=0.717^{+0.009}_{-0.009}$, $\\Omega_{m,0}=0.333$, $\\Omega_{k,0}=0.003$, $\\xi=-0.342$, $\\sigma_8=0.760$, and $S_8=0.801\\pm0.150$; the other models give similar $h$ and $S_8\\approx0.785$ and $0.773$. The authors read these results as showing that the negative torsion-scalar coupling, rather than curvature alone, drives the improvement, and that nonflat teleparallel dark energy can ease both the Hubble and the $S_8$ tensions relative to Planck-$\\Lambda$CDM.","pith_inferences":["The decisive $\\Delta\\mathrm{AIC}$ for the vanishing-potential scenario should be tested against an extended dataset that includes CMB distance priors or BAO, since those probes constrain curvature and expansion at redshifts where the torsion-scalar coupling may behave differently.","If the full Hamiltonian analysis called for in the paper's final remark reveals additional strong-coupled degrees of freedom on FLRW backgrounds, those modes could back-react on the background and alter the posteriors, so the observational success is not guaranteed to survive the more complete theory.","A direct extension would replace the flat-space quasi-static $G_{\\mathrm{eff}}$ with a self-consistent curved-background derivation and run N-body or higher-order perturbation simulations; the predicted $f\\sigma_8(z)$ at $z\\lesssim1$ could then be compared directly with upcoming redshift-space distortion surveys."],"forward_implications":["If the vanishing-potential result holds, $\\Lambda$CDM would be statistically outperformed by a torsion-based scalar field with nonzero spatial curvature, by a margin conventionally read as decisive.","The Hubble constant in all three teleparallel dark energy scenarios sits near $h \\approx 0.717$, in $1\\sigma$ agreement with SH0ES and more than $4\\sigma$ away from the Planck value, so the Hubble tension would be substantially eased without invoking early-universe physics.","The inferred $S_8$ values fall below Planck's $0.832$ and overlap better with low-redshift large-scale-structure measurements, easing the growth-tension side as well.","The mild preference for $\\Omega_{k,0}>0$ means curvature is not required by the data; the negative torsion-scalar coupling $\\xi$ is the parameter doing the main work.","The exponential- and power-law-potential variants remain statistically comparable to $\\Lambda$CDM, so the strong preference is specific to the zero-potential scenario rather than generic to the framework."],"supporting_citations":[{"why":"Sets up the flat-space nonminimal scalar-torsion model whose cosmological analysis this paper generalizes to $k\\neq0$; also supplies the initial-condition and integration strategy.","marker":"[56]"},{"why":"Introduces teleparallel dark energy as a scalar field nonminimally coupled to the torsion scalar, the framework used throughout.","marker":"[53]"},{"why":"Establishes the tetrad-spin connection equivalence that justifies using the diagonal tetrad and the torsion scalar $T=-6(H^2-k/a^2)$ in nonflat FLRW.","marker":"[49]"},{"why":"Provide the flat-space quasi-static expression for $G_{\\mathrm{eff}}$ that Eq. (26) adopts and that carries the perturbation-sector claims.","marker":"[50, 55]"},{"why":"Supply the Pantheon+ supernova sample (1701 light curves) that dominates the background likelihood.","marker":"[78, 79]"},{"why":"Provide the SH0ES Cepheid host-distance calibration that anchors the reported high $h$ values.","marker":"[80]"},{"why":"Supplies the 31 cosmic chronometer Hubble measurements used in the joint likelihood.","marker":"[83]"},{"why":"Provides the 18 $f\\sigma_8$ growth-rate measurements and the $\\Lambda$CDM-fiducial correction procedure used to constrain $S_8$.","marker":"[84]"},{"why":"Defines the Planck-$\\Lambda$CDM baseline values for $h$, $\\Omega_m$, $\\Omega_k$, and $S_8$ against which the paper's results are compared.","marker":"[88]"},{"why":"Define the AIC and DIC model-comparison statistics whose $\\Delta$ values carry the preference claims.","marker":"[89, 90]"}],"fun_headline_variants":["Teleparallel dark energy outdoes ΛCDM by 10 AIC points","Nonflat teleparallel model eases Hubble and S8 tensions","Torsion-scalar coupling beats ΛCDM in combined datasets","Open teleparallel dark energy fits data better than ΛCDM","V=0 teleparallel dark energy favored over ΛCDM"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The growth-rate and $S_8$ results rest on assuming the flat-space quasi-static formula $G_{\\mathrm{eff}}$ remains valid in a spatially curved FLRW background whenever the curvature scale is much larger than the perturbation scale; the paper asserts rather than derives this, and its own final remark concedes that strong-coupling issues may make linear perturbation analyses around symmetric teleparallel backgrounds incomplete.","fun_headline_variants_meta":{"raw":{"variants":["Teleparallel dark energy outdoes ΛCDM by 10 AIC points","Nonflat teleparallel model eases Hubble and S8 tensions","Torsion-scalar coupling beats ΛCDM in combined datasets","Open teleparallel dark energy fits data better than ΛCDM","V=0 teleparallel dark energy favored over ΛCDM"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000638,"raw_usage":{"total_tokens":3003,"prompt_tokens":1070,"completion_tokens":1933,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":686,"completion_tokens_details":{"reasoning_tokens":1842}},"tokens_in":686,"tokens_out":1933,"duration_ms":14645,"temperature":1.0,"reasoning_tokens":1842,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:30:26.372488+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Deriving the full linear scalar perturbations in covariant teleparallel gravity on a nonflat FLRW background would settle the matter: if the Poisson equation acquires a correction of order $k/(a^2H^2)$ relative to Eq. (26), the reported $S_8$ and $\\Delta\\mathrm{AIC}$ values would shift; alternatively, re-running the MCMC without the growth-rate data tests whether the decisive $\\Delta\\mathrm{AIC}=-10.4$ preference survives without the assumed $G_{\\mathrm{eff}}$.","supporting_citations":[],"review_version":1}