{"id":"97e13cd4-3400-4aae-b40a-5bfc877d0c77","arxiv_id":"2502.10466","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A compilation of f(Q) and f(Q,T) gravity models that fit late-time cosmic acceleration data, reproducing quintessence, phantom, and Lambda-CDM-like behavior without a cosmological constant.","lead":"This PhD thesis compiles several studies of modified symmetric teleparallel gravity, f(Q) and f(Q,T), applied to the late-time acceleration of the Universe. The models are fitted to supernova, Hubble, and BAO data and can mimic dark energy, but they rely on ad hoc viscosity and connection choices.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Pantheon chi-square marginalization in Sec. 2.5.2 is self-contradictory (B equals A), so the quoted fits and contours may be biased; the central late-time-acceleration claim depends on these fits and needs a recomputation.","rationale":"The reader's weakest_assumption concerns the ad hoc choices of viscosity, γ(t), and the H(z) parameterization. That is a legitimate model-building concern, but it is not the single most load-bearing issue for the central claim: ad hoc forms can still be used to fit data, and the thesis explicitly presents the models as proposals. The chi-square marginalization error is more load-bearing because it threatens the internal validity of the data fits that are the direct evidence for the acceleration claim. If the formula is wrong, the fitted parameters and the derived transition redshift are unreliable regardless of the status of the functional forms. The concrete test would settle this immediately. The reader did note the chi-square error as a secondary issue, so my concern partially overlaps with the reader's but is not the one identified as weakest.","tokens_in":60651,"tokens_out":7164,"duration_ms":64533,"concrete_test":"Recompute the Chapter 2 Pantheon likelihood with the correct marginalization: set B = Σ_i [μth(μ0=0,z_i,θ) − μobs(z_i)]/σ_i² (no square), keep A and C as printed, and rerun the emcee MCMC with the same priors and data. Compare the best-fit values and 1σ/2σ contours with Figs. 2.7 and 2.10. If the parameter shifts exceed the quoted 1σ uncertainties, or if the joint contours move appreciably, the reported fits do not support the acceleration claim as stated. Also check the analysis scripts to see whether the printed B (squared) or the correct B (unsquared) was used; if the correct one was used, the text is a typo but the reproducibility issue remains.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. 2.5.2, the thesis derives the Pantheon chi-square. It defines χ²(μ0, θ) = Σ_i [μth(μ0,z_i,θ) − μobs(z_i)]²/σ_i², then asserts that after marginalizing the additive nuisance μ0, χ²(θ) = A − B²/C, with A = Σ_i [μth(μ0=0,z_i,θ) − μobs(z_i)]²/σ_i², B = Σ_i [μth(μ0=0,z_i,θ) − μobs(z_i)]²/σ_i², C = Σ_i 1/σ_i². The expression for B is identical to A; the standard marginalization for a shift in distance modulus requires B = Σ_i [μth(μ0=0,z_i,θ) − μobs(z_i)]/σ_i² (no square). If the supplied formula was used in the MCMC analysis, the 'marginalized' likelihood is not the likelihood marginalized over μ0, and the resulting best-fit parameters (α = −1.33, ξ0 = 0.10, ξ1 = 1.81, ξ2 = 2.08), the 1σ–2σ contours (Fig. 2.7), and the combined BAO results (Figs. 2.9–2.10) are not valid. Because the abstract's claim that the model 'can effectively describe the acceleration of the cosmic expansion' is based on these fits, the central claim is not reproducible as written.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The thesis (arXiv:2502.10466) develops cosmological models in modified symmetric teleparallel gravity. It derives exact Hubble solutions for linear and power-law f(Q) gravity with bulk viscous fluids, fits the resulting models to Hubble, Pantheon, BAO, and Pantheon+SH0ES data, and uses the fits to claim a late-time deceleration-to-acceleration transition and quintessence, phantom, and Lambda-CDM-like effective behavior. It also presents a non-coincident connection framework with a parameterized Hubble function, applies energy conditions and sound-speed stability tests to several STEGR corrections, and closes with a covariant formulation and phase-space analysis of f(Q,T) gravity. The abstract explicitly concedes that the bulk-viscous solutions cannot describe the early Universe.","tokens_in":61102,"tokens_out":6514,"duration_ms":70846,"significance":"If the statistical results can be made reproducible, the thesis would be a useful collection of exact f(Q) cosmologies: the field-equation manipulations and analytical integrations are largely self-consistent, the non-coincident connection calculations in Chapter 5 go beyond the usual coincident-gauge treatment, and the f(Q,T) covariant formulation in Chapter 6 is a valuable reference point. The manuscript also has the merit of being explicit about its main limitation, namely that the bulk-viscous solutions fail in the early Universe. However, the central late-time claims currently rest on a printed chi-square marginalization that is algebraically wrong, and the Chapter 4 conclusions are obtained by fixing model parameters to the very observables the model is then said to reproduce. These issues must be addressed before the data-driven conclusions can be accepted.","major_comments":[{"comment":"The quantities A and B are printed identically: B is defined as the same sum of squared residuals as A. For a Gaussian marginalization over an additive nuisance mu0, the correct profile chi-square is A - B^2/C with B = sum_i [mu_th(mu0=0,z_i,theta)-mu_obs(z_i)]/sigma_i^2, i.e., the linear residual, not the squared residual. As written, the 'marginalized' chi-square is A - A^2/C, which is not the likelihood marginalized over mu0 and can bias the parameter estimates. The Pantheon best-fit values (alpha=-1.33, xi0=0.10, xi1=1.81, xi2=2.08), the contours in Figs. 2.7 and 2.10, and the statefinder statements based on those parameters are therefore not reproducible from the text. This must be corrected and the fits rerun before the Chapter 2 claim of describing late-time acceleration can be evaluated.","section":"Sec. 2.5.2, Eq. (2.28) and the following display"},{"comment":"The parameters alpha and beta are fixed by solving Eqs. (4.22) and (4.23) using the observed values H0=67.9 km/s/Mpc, q0=-0.55, and Omega0=0.303, and the subsequent sections then show that the model reproduces quintessence, phantom, or Lambda-CDM-like behavior for different choices of n. This is a demonstration that the ansatz can be tuned to the target observables, not an independent observational validation. No MCMC fit with propagated uncertainties is presented for the n>=1 and n<=-1 cases. The text should either reframe Sections 4.4-4.6 as existence/tuning examples or perform a genuine data fit and report the resulting parameter uncertainties.","section":"Sec. 4.4-4.6, Eqs. (4.22)-(4.23)"},{"comment":"The Hubble parameterization H(z)=H0(z+1)^n + beta[1-(z+1)^n] and the connection function gamma(t)=-a^{-1}Hdot are assumed without derivation from the f(Q) action or from microphysics. All subsequent constraints on Models I-V via energy conditions and sound speed are therefore conditional on these choices. The text should state this limitation explicitly and, ideally, test robustness by considering alternative parameterizations of H(z) or alternative non-constant gamma(t), since a different ansatz will in general change the fitted parameters, the transition redshift, and the derived energy-condition profiles.","section":"Sec. 5.2, Eq. (5.12)"},{"comment":"The Pantheon likelihood in Eq. (3.13) uses only the diagonal errors sigma(zk) and does not show the standard marginalization over the absolute magnitude nuisance parameter. The Pantheon release includes a full covariance matrix with systematic uncertainties, and the usual analysis either uses that covariance or explicitly marginalizes over M. As printed, the reported 1-sigma contours in Fig. 3.4 are likely optimistic. Please clarify the treatment of systematics and either use the full covariance or state and justify the diagonal approximation.","section":"Sec. 3.3.3, Eq. (3.13)"}],"minor_comments":[{"comment":"The statement that DeltaBIC=6.869 constitutes 'strong evidence' is inconsistent with the thresholds given in the same paragraph, where 2-6 is called moderate and >10 is called no support. Please correct the interpretation or the threshold convention.","section":"Sec. 5.3.3"},{"comment":"The evolutionary profiles of H, q, rho, p, omega, and the energy conditions are plotted only as central curves. Adding 1-sigma and 2-sigma bands propagated from the MCMC chains would make the fits quantitatively comparable and would strengthen the claims about the deceleration-to-acceleration transition.","section":"Figs. 3.5-3.12 and 5.2"},{"comment":"Several typographical errors should be corrected in a revised version: 'Reimannian' for 'Riemannian', 'charateristics' for 'characteristics', 'Ries' for 'Riess', and the spacing in 'T ee-How' and 'W eak'.","section":"Throughout"},{"comment":"The abstract's admission that the bulk-viscous solutions cannot describe the early phases is an important scope limitation and should be restated in the concluding chapter rather than only in the abstract, so that readers do not over-interpret the late-time fits as a complete cosmological model.","section":"Abstract and Sec. 7.1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a PhD thesis compiled from previously published papers, and the arXiv text contains many OCR-style artifacts and garbled axis labels. My main concern for the editor is reproducibility: the Chapter 2 Pantheon analysis contains an algebraic error in the printed marginalization formula, and without a code/data release or a corrected calculation the central data-driven claim cannot be independently verified. I therefore recommend major revision rather than rejection, because the analytical framework is coherent and the issues are fixable by rerunning the fits and reframing several claims as conditional or tuned examples."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The honest summary: this is a PhD thesis that assembles the author's own published papers into one document. The core results—viscous f(Q) solutions, the αQ+βQ^n constraints, the non-coincident Hubble parameterization—are not new relative to those papers. What the thesis does well is present them coherently, with the derivations mostly consistent and the analytical solutions checked against data. It also states plainly that these models do not describe the early Universe, which is a real limitation acknowledged up front. For someone entering f(Q) cosmology, this is a serviceable starting point.\n\nThe soft spot that matters is in Sec. 2.5.2. The Pantheon chi-square marginalization formula defines B identically to A—both have the squared residual. The standard marginalization over the additive nuisance μ0 requires B = Σ [μth(μ0=0) − μobs]/σ², without the square. As written, the formula is self-contradictory. If that formula was actually used in the MCMC, the quoted best-fit parameters and contours in Chapter 2, and by extension the abstract's claim about describing cosmic acceleration, are not reproducible. This is a load-bearing statistical error, not a typo you can wave off. The underlying published paper (Phys. Dark Univ. 32, 100820) may have had it right, but this thesis as posted does not.\n\nOther soft spots are lighter. Chapters 4 and 5 fix parameters from the same data they then compare against, so this is fitting rather than prediction—common in this literature, and the thesis does not aggressively oversell it. The viscosity ansatz and the connection function γ(t) = −a⁻¹Ḣ are hand-picked, with no derivation from microphysics or the f(Q) action. That limits how strongly you can interpret the 'predictions.' Minor: the evolutionary profiles in later chapters lack uncertainty bands.\n\nBottom line: the central idea that bulk viscosity in f(Q) gravity can mimic late-time acceleration is plausible and consistent with earlier work, but the statistical validity of the headline fits is compromised as written. The thesis deserves a serious referee only if the chi-square issue is fixed first. For my own work, I would cite the original journal articles, not this arXiv posting—though I might point a starting student to it for the broad overview.","headline":"A usable thesis compilation of already-published f(Q) cosmology papers, but a wrong chi-square marginalization formula in Chapter 2 undermines the headline data fits as written.","tokens_in":654,"tokens_out":795,"would_cite":false,"duration_ms":38543,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83F05"],"pacs":["04.50.Kd","98.80.-k","98.80.Es"],"model":"deepseek-v4-flash","headline":"This thesis argues that modified non-metricity gravity plus bulk viscosity can reproduce the observed late-time cosmic acceleration without a cosmological constant, while conceding the solutions fail in the early Universe.","keywords":["modified symmetric teleparallel gravity","f(Q) gravity","f(Q,T) gravity","non-metricity","bulk viscosity","dark energy without cosmological constant","late-time cosmic acceleration","observational cosmology"],"falsifier":"A concrete falsifier: extrapolate the fitted $H(z)$ from the non-coincident formalism to last scattering and compute the CMB acoustic angular scale and primordial element abundances. Because the thesis concedes that the solutions cannot describe early phases, those predictions should disagree with measured CMB distances; showing the size of that disagreement would settle whether the model is only a late-time fit.","tokens_in":60442,"feed_emoji":"🌌","tokens_out":11081,"duration_ms":101462,"temperature":0.7,"pith_summary":"This PhD thesis sets out to show that a family of modified gravity theories built on non-metricity — f(Q) gravity and its f(Q,T) extension — can account for the observed late-time acceleration of the Universe without a cosmological constant or an exotic dark-energy fluid. The author constructs exact cosmological solutions in which bulk viscosity supplies negative pressure, constrains their free parameters with Hubble, Pantheon, BAO, and Pantheon+SH0ES datasets, and finds the resulting models reproduce quintessence, phantom, and ΛCDM-like expansion histories. The central positive claim is that the models fit the low-redshift expansion data and predict a recent deceleration-to-acceleration transition. The thesis is equally explicit about its limit: these solutions cannot describe the early phases of the Universe.","feed_headline":"Modified gravity plus viscosity reproduces cosmic acceleration","feed_subtitle":"It fits Hubble, supernova, and BAO data at late times while conceding the early universe is out of reach.","key_machinery":"The load-bearing object is the non-metricity scalar $Q$, defined by contraction of the non-metricity tensor that measures how much a connection fails to preserve the metric. In a flat FLRW background in the coincident gauge, $Q=6H^2$, so the modified action $S=\\int f(Q)\\sqrt{-g}\\,d^4x$ generates Friedmann-like equations whose extra geometric terms act as an effective dark-energy fluid. Two auxiliary mechanisms carry the derivations: a bulk-viscosity effective pressure $\\bar p=p-3\\xi H$ with the assumed viscosity $\\xi=\\xi_0+\\xi_1H+\\xi_2(\\dot H/H+H)$, which produces negative pressure without exotic matter; and, in the non-coincident formalism, a non-vanishing connection function $\\gamma(t)=-a^{-1}\\dot H$ that changes the Friedmann equations and makes the theory genuinely distinct from $f(T)$ gravity. The model-independent Hubble parameterization $H(z)=H_0(1+z)^n+\\beta[1-(1+z)^n]$ then supplies a closed-form expansion history that can be fitted to data and used to test the energy conditions.","core_discovery":"On the paper's own terms, the discovery is that the non-metricity scalar $Q$ can play the role usually assigned to dark energy. For the linear model $f(Q)=\\alpha Q$ with a bulk-viscous matter fluid, the viscosity coefficient $\\xi=\\xi_0+\\xi_1H+\\xi_2(\\dot H/H+H)$ yields an analytic $H(z)$ that fits 57 Hubble points, 1048 Pantheon supernovae, and six BAO points, driving $q$ from deceleration to acceleration in the recent past. For the non-linear power-law model $f(Q)=\\alpha Q^n$, the effective pressure becomes negative at low redshift, the deceleration parameter shows a transition at $z_t\\approx 0.14$–$0.78$ depending on dataset, and the energy conditions NEC/WEC/DEC hold while SEC is violated. For $f(Q)=\\alpha Q+\\beta Q^n$ in the coincident gauge, the geometric dark-energy component behaves as quintessence for $n\\ge 1$, phantom for $n\\le -1$, and $\\Lambda$CDM for $n=0$, with the case $f(Q)=\\alpha Q+\\beta$ constrained to $\\alpha=0.998760\\pm0.000048$, $\\beta=-26.01\\pm0.98$ and transition redshift $z_t=0.844$. In the non-coincident formalism, a non-constant connection $\\gamma(t)=-a^{-1}\\dot H$ gives Friedmann equations distinct from $f(T)$ theory, and the parameterization $H(z)=H_0(1+z)^n+\\beta[1-(1+z)^n]$ fits CC+Pantheon+SH0ES+BAO with $H_0=68\\pm0.094$ km/s/Mpc, $q_0=-0.388\\pm0.002$, $z_t=0.857\\pm0.011$. The author's stated bottom line is that geometry alone can generate the late-time acceleration, with the caveat that the same solutions do not extend to the early Universe.","pith_inferences":["Editorial inference: because the fitted forms for $\\xi$, $f(Q)$, and $H(z)$ are chosen rather than derived, the numerical constraints, such as $H_0=68\\pm0.094$ km/s/Mpc and $z_t=0.857\\pm0.011$, should be read as attached to those ansatze; a different equally reasonable choice could shift the best-fit values by more than the quoted $1\\sigma$ errors.","Editorial inference: the same parameterization machinery could be extended to early-Universe probes such as CMB acoustic-scale distances or primordial nucleosynthesis abundances; the thesis's own admission that the solutions fail at early times suggests such an extension would be the immediate stress test.","Editorial inference: the connection function $\\gamma(t)=-a^{-1}\\dot H$ is itself an ansatz; exploring other non-constant $\\gamma(t)$ choices would show whether the claimed late-time fits are robust features of non-coincident $f(Q)$ gravity or artifacts of this particular gauge connection."],"forward_implications":["If the central claim is right, late-time cosmic acceleration can be obtained from geometry plus viscosity, so a cosmological constant is not the only viable explanation of the supernova data.","The fitted models predict a recent transition from decelerated to accelerated expansion (transition redshift roughly $z_t\\simeq0.14$–$0.86$ depending on model and dataset), which can be compared against future high-redshift expansion-rate measurements.","The $\\alpha Q+\\beta Q^n$ class gives a single geometric dark-energy fluid that interpolates between quintessence ($n\\ge1$), phantom ($n\\le-1$), and $\\Lambda$CDM ($n=0$) behavior, meaning one family of actions covers the main dark-energy phenomenologies.","The non-coincident connection with $\\gamma(t)=-a^{-1}\\dot H$ yields Friedmann equations that are not equivalent to $f(T)$ gravity, so parameter constraints obtained in this formalism are new information rather than a re-derivation of known results.","The explicit caveat that these solutions cannot describe the early Universe implies the models are late-time effective descriptions only, not full cosmic histories."],"supporting_citations":[{"why":"This citation introduces the f(Q) modification of symmetric teleparallel gravity, the theory underlying every model in the thesis.","marker":"[57]"},{"why":"This citation provides the extension of symmetric teleparallel gravity that supplies the f(Q) field equations and Friedmann-like equations.","marker":"[89]"},{"why":"This citation supplies the bulk viscosity ansatz xi=xi0+xi1H+xi2(Hdot/H+H) used to generate negative pressure in Chapters 2 and 3.","marker":"[116]"},{"why":"This citation gives the Pantheon 1048-point Type Ia supernova sample used to constrain model parameters in Chapters 2 through 4.","marker":"[19]"},{"why":"This citation gives the updated 57-point Hubble dataset, combining differential-age and BAO measurements, used for H(z) fits.","marker":"[136]"},{"why":"This citation gives the BAO chi-square with covariance matrix used in Chapters 2 and 3 for the six-point BAO sample.","marker":"[140]"},{"why":"This citation introduces the non-coincident affine connection with a non-constant gamma(t) that underlies Chapter 5's distinct Friedmann equations.","marker":"[203]"},{"why":"This citation supplies the Pantheon+SH0ES 1701-point sample and its covariance matrix used for the Chapter 5 MCMC constraints.","marker":"[216]"},{"why":"This citation motivates the polynomial and exponential f(Q) functional forms and supplies comparative energy-condition results.","marker":"[90]"},{"why":"This citation defines the statefinder diagnostic pair (r,s) used to distinguish the models from Lambda-CDM.","marker":"[141]"}],"fun_headline_variants":["Modified gravity with viscosity mimics dark energy","Non-metricity gravity reproduces cosmic acceleration","Viscous f(Q) gravity fits supernova and Hubble data","Geometry alone drives late-time cosmic expansion","f(Q) gravity plus viscosity explains accelerated expansion"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole construction rests on hand-picked mathematical forms for the viscosity, the $f(Q)$ function, the connection function, and the Hubble parameterization, and the numerical results would change if those forms were replaced, since none of them is derived from the action or from microphysics.","fun_headline_variants_meta":{"raw":{"variants":["Modified gravity with viscosity mimics dark energy","Non-metricity gravity reproduces cosmic acceleration","Viscous f(Q) gravity fits supernova and Hubble data","Geometry alone drives late-time cosmic expansion","f(Q) gravity plus viscosity explains accelerated expansion"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000221,"raw_usage":{"total_tokens":1560,"prompt_tokens":1164,"completion_tokens":396,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":780,"completion_tokens_details":{"reasoning_tokens":325}},"tokens_in":780,"tokens_out":396,"duration_ms":3939,"temperature":1.0,"reasoning_tokens":325,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T05:35:59.887865+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete falsifier: extrapolate the fitted $H(z)$ from the non-coincident formalism to last scattering and compute the CMB acoustic angular scale and primordial element abundances. Because the thesis concedes that the solutions cannot describe early phases, those predictions should disagree with measured CMB distances; showing the size of that disagreement would settle whether the model is only a late-time fit.","supporting_citations":[{"cited_title":"Dimakis et","cited_arxiv_id":null,"evidence_quote":"This citation introduces the non-coincident affine connection with a non-constant gamma(t) that underlies Chapter 5's distinct Friedmann equations."}],"review_version":1}