Cosmic reverberations on a constrained $ f(Q,T) $-model of the Universe

Akanksha Singh; Ertan G\"udekli; J. K. Singh; Shaily

REVIEW 4 major objections 5 minor 136 references

Cosmic reverberations on a constrained $ f(Q,T) $-model of the Universe

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A constrained f(Q,T) gravity model claims to ease the Hubble tension and to replace the Big Bang singularity with an ekpyrotic brane collision.

desk verdict An analytically complete but kinematically driven f(Q,T) paper whose H0-tension claim is spoiled by a double-counted likelihood and whose ekpyrotic/inflationary interpretations are overstated. read the letter →

arxiv 2412.12210 v2 pith:NNMYMTM6 submitted 2024-12-15 gr-qc astro-ph.CO

Akanksha Singh , Shaily , J. K. Singh , Ertan Güdekli This is my paper · ORCID

classification gr-qcastro-ph.CO MSC 83D0583F05 PACS 98.80.Cq

keywords f(QT)gravitynon-metricityHubbletensionekpyroticphasequintessencejerkparameterdeceleration-to-accelerationtransitionPantheondataset

topics Dark Energy The Hubble Tension

open problems Dark Energy The Hubble Tension

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

The paper tries to establish that a specific quadratic f(Q,T) gravity model, with f(Q,T)=ζQ²+γT, can reproduce the observed expansion history once one assumes a particular form for the jerk parameter. Fitting to 77 cosmic-chronometer H(z) points and 1048 Pantheon supernovae gives H0=69.99999±0.0001, a middle value that the authors say reduces the Hubble tension. The same model yields an ekpyrotic pre-Big-Bang phase above redshift z=12.32 and a late-time quintessence phase, so a single modified-gravity function would connect the H0 tension, the origin of the universe, and cosmic acceleration without a cosmological constant. The key caveat, stated in the construction, is that the expansion history is imposed by the jerk ansatz rather than solved from the field equations.

What carries the argument

The load-bearing object is the kinematic jerk ansatz: Eq. (18) defines j(z)=q(z)+2q(z)²+(1+z)dq/dz, and the paper sets j(z)=1+q(z)+q²(z)/2, the first three Maclaurin terms of e^q. Solving this first-order differential equation yields q(z), and then the relation q(z)=-1+(1+z)(dH/dz)/H gives the closed-form Hubble parameter H(z) shown in Eq. (22). The f(Q,T) action with f=ζQ²+γT (n=2, m=1) supplies the generalized Friedmann equations that convert this H(z) into energy density and pressure, and all subsequent results—transition redshifts, energy conditions, scalar-field potentials, slow-roll parameters—are read off those expressions.

What would settle it

Solve the f(Q,T)=ζQ²+γT field equations directly for H(z) without the jerk ansatz, using the same ζ=-1.82, γ=-0.9 and the same likelihoods, and compare the best-fit H0 and transition redshift with the paper's values; alternatively, measure the jerk parameter j(z) from an independent high-redshift cosmic-chronometer or BAO sample and check whether it equals 1+q+q²/2. A mismatch would settle that the claimed H0 value and the ekpyrotic phase are artifacts of the assumed ansatz rather than consequences of f(Q,T) gravity.

Watch

Extended reading notes

Core claim

The paper claims that in flat FLRW spacetime within f(Q,T) gravity, taking f(Q,T)=ζQ²+γT and choosing the jerk parameter as j(z)=1+q(z)+q²(z)/2 fully determines the deceleration and Hubble parameters. Constraining the two free constants with the OHD and Pantheon datasets gives H0=69.99999±0.0001 from the joint fit, a value the authors interpret as easing the H0 tension when compared with other modified-gravity results and with ΛCDM. The same kinematics produces an equation of state ω>>1 at z>12.32, which the authors identify with an ekpyrotic contracting phase whose Big Bang is a brane collision rather than the beginning of time, and a late-time phase with -1<ω<-1/3, characterizing quintessence dark energy. The f(Q,T) field equations are used not to determine H(z) but to reconstruct ρ, p, energy conditions, scalar-field kinetic and potential terms, and slow-roll parameters from the assumed H(z).

Load-bearing premise

The expansion history is imposed by choosing the jerk parameter to be 1+q+q²/2; the f(Q,T) field equations never determine H(z), so every result—the fitted H0, the transition redshift, the ekpyrotic and quintessence phases—rests on that untested kinematic choice.

Editorial extensions

If this is right

The joint OHD+Pantheon fit pins H0 at 69.99999 with sub-0.0002 reported errors, a value between CMB and local distance-ladder estimates, which the authors take as easing the Hubble tension.
The model predicts a deceleration-to-acceleration transition at ztr=6.39 for the joint dataset, much earlier than the standard ΛCDM transition near z≈0.6, so it makes a distinctive prediction for future high-redshift probes.
At z>12.32 the equation of state satisfies ω>>1, interpreted as an ekpyrotic phase with a brane-collision 'Big Bang', meaning the initial singularity is not the beginning of time in this model.
At late times the model behaves as quintessence with -1<ω<-1/3 and violates the strong energy condition, consistent with present-day cosmic acceleration without a cosmological constant.
The model deviates from ΛCDM at early times (j does not equal 1) but converges to ΛCDM behavior at late times in the H(z) and distance-modulus plots.

Reading between the lines

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

Inference: because H(z) is fixed by the jerk ansatz rather than by the f(Q,T) dynamics, the same expansion history could be embedded in many gravity theories; the claimed H0 value likely tests the kinematic ansatz more than it tests f(Q,T) gravity itself.
Inference: replacing the ad hoc jerk form with a theoretically motivated one, for example from a scalar-tensor or effective-loop model, would provide a direct template for translating any j(z) into a full f(Q,T) cosmology and would show whether the ekpyrotic and quintessence phases survive.
Inference: the tiny reported error on H0 reflects fitting the chosen datasets with a two-parameter function, not cosmological certainty; adding BAO or CMB data could shift the central value and substantially enlarge the error bars.
Inference: a sharper observational test is to compare the predicted very early transition redshift and the pressure sign-change redshift with independent tracers of the matter-to-acceleration crossover; standard dark-energy probes would likely constrain such an early transition if it is not specific to the Pantheon sample.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take on 2412.12210. The paper's headline—that a constrained f(Q,T) model reduces the H0 tension to 69.99999 ± 0.0001—is not credible, but not for the reason in the stress test. The stress test claims H0 cancels in the distance modulus. It doesn't: with μ = 5 log10 D_L + μ0 and μ0 = 5 log10(H0^{-1}) + 25, and D_L ∝ H0^{-1}, the H0 terms add, giving -10 log10 H0. The likelihood does depend on H0, but the formula double-counts it. That, combined with a fixed α, is probably why the MCMC spits out 10^-4 uncertainties. The real problem is that the expansion history is not derived from the f(Q,T) field equations; it is set by an assumed jerk function j = 1 + q + q²/2 (from a Maclaurin expansion of exp(q)). The field equations are then only used to compute ρ and p. So the "constraints" test the jerk ansatz, not the gravity theory.

What is useful: the authors carry through a complete analytic treatment—exact H(z), ρ(z), p(z), a scalar-field description, slow-roll parameters, energy conditions—and compare against OHD and Pantheon in a standard way (modulo the H0 double-count). For a reader who wants to see the machinery of f(Q,T) cosmology applied to a kinematical ansatz, it is a reasonable template. The table comparing H0 across modified gravity models is a handy summary.

Soft spots beyond the likelihood: the ekpyrotic claim is a mislabel. The model has an expanding universe with ω >> 1 at high z; there is no contracting branch, so calling it ekpyrotic (and the brane-collision Big Bang) is importing Lehners's scenario without the dynamics. The slow-roll analysis evaluates ε1, ε2 at z → -1, the far future, and calls it inflation; inflation should be at early times. Those two interpretive steps are the paper's main scientific overreach.

Who it's for: people working in f(Q,T) phenomenology, maybe as a baseline for a better likelihood treatment. I would not cite it. It deserves a referee—the errors are specific and fixable—but the referee will likely ask for a corrected likelihood, a reframing that does not claim to constrain f(Q,T), and removal or justification of the ekpyrotic and inflation interpretations. If they fix those, there might be a modest paper here.

Referee Report

4 major / 5 minor

Summary. The paper constructs a flat FLRW cosmological model in f(Q,T) gravity with f(Q,T)=ζQ²+γT. The dynamical expansion history is not obtained from the f(Q,T) field equations; instead the authors assume a kinematic jerk ansatz, j(z)=e^{q(z)}≈1+q(z)+q²(z)/2, solve the resulting differential equation for q(z), and integrate to obtain H(z). They then fit the free parameters α and H0 to the OHD, Pantheon, and joint datasets, and use the fitted H(z) to compute ρ, p, the equation of state, energy conditions, a quintessence-like scalar field, and slow-roll parameters. The paper claims a deceleration-to-acceleration transition, a quintessence phase at late times, an ekpyrotic phase at z>12.32 in which the Big Bang is a brane collision, and a reduction of the H0 tension with H0≈70.0 from the joint fit.

Significance. If the claims were valid, the paper would show that a specific f(Q,T) gravity model can fit the background expansion history and, through the recovered H0≈70 km/s/Mpc, mitigate the Hubble tension. The manuscript has some strengths: the field equations are written out explicitly, the algebraic derivation of ρ and p from the assumed H(z) is transparent, public OHD and Pantheon data are used, and comparisons with ΛCDM and several other modified-gravity models are provided. However, the central results are not supported. The expansion history is fixed by an ad hoc jerk ansatz rather than by the modified-gravity dynamics; the Pantheon likelihood as written cannot produce the reported H0 constraints; the coupling constants ζ and γ are set by hand; and the ekpyrotic and slow-roll interpretations rest on conceptual misapplications. These issues affect the paper's main quantitative and qualitative conclusions, not merely their presentation.

major comments (4)

[III, Eqs. (24)–(27); Table II] The Pantheon likelihood cannot support the H0 values reported in Table II. Writing H(z)=H0 f(z), Eq. (25) gives D_L=(1+z)c∫dz'/H = H0^{-1}(1+z)c∫dz'/f, so D_L is proportional to H0^{-1}. Equation (26) then introduces a second H0^{-1} factor through μ0. Read literally, the two H0 factors do not cancel; they enter as −5log10H0 and −5log10H0, so the resulting χ²_PDS is a double-counted, dimensionally inconsistent function of H0. If, instead, the intended convention is the standard one in which H0 appears only in μ0, then the Pantheon sample with an uncalibrated absolute magnitude cannot constrain H0 at all. In either reading, the Pantheon-only value H0=69.99998±0.0001 and the joint value H0=69.99999±0.0001 are not supported by the written likelihood. Since the abstract and Section V base the claimed H0-tension reduction on exactly these numbers, this is a load-bearing error.
[II, Eq. (18) and the paragraph after it] The expansion history H(z) is not derived from the f(Q,T) field equations. The paper assumes j(z)=e^{q(z)} and then approximates it by 1+q+q²/2, solves the resulting differential equation for q(z), and integrates to get H(z) in Eq. (22). The field equations (14)–(17) are used only afterward, to convert this assumed H(z) into ρ and p. Consequently, the deceleration-to-acceleration transition redshifts, the equation-of-state phases, the ekpyrotic boundary z>12.32, and the quintessence behavior are properties of the assumed jerk ansatz and the fitted α, not independent predictions of f(Q,T) gravity. The abstract and Section V present these quantities as outcomes of the constrained f(Q,T) model, which is not justified by the derivation.
[IV, Fig. 4 caption; III, Table II] The coupling constants ζ and γ are fixed by hand, with ζ=−1.82 and γ=−0.9 used in Fig. 4, and they are never constrained by the data or derived from any theoretical condition. All of the derived physical quantities—ρ, p, ω, the energy conditions, and the scalar-field kinetic and potential terms—depend on these arbitrary values through Eqs. (16) and (17). The qualitative conclusions, including the claimed ekpyrotic phase and quintessence phase, are therefore not robust predictions of a constrained model. The paper should either constrain ζ and γ jointly or demonstrate that the conclusions are insensitive to their values over a well-motivated range.
[IV, Table III and Fig. 4c] The identification of an ekpyrotic phase is not supported by the model. The ekpyrotic scenario (ref. [55]) involves a slow contraction phase before the Big Bang, with the Big Bang described as a brane collision. In this paper, H(z) from Eq. (22) is positive for all z≥0, describing an expanding universe, and the model contains no contracting branch or brane-collision dynamics. The appearance of ω≫1 at high redshift in an expanding FLRW model does not constitute an ekpyrotic phase, and the statement that 'the Big Bang is not the beginning of time' is an extrapolation from the assumed EoS rather than a consequence of the f(Q,T) equations.

minor comments (5)

[III, Eq. (26)] Equation (26) is dimensionally inconsistent: H0^{-1} has units of time (or Mpc s/km), not Mpc, and the combination 5Log10(H0^{-1}/1Mpc)+25 mixes units. The standard route is to define a dimensionless reduced luminosity distance d_L=(1+z)∫dz'/E(z') and set μ0=5log10(c/H0/Mpc)+25.
[III, Table II] The Pantheon and joint H0 uncertainties of about 10^-4 km/s/Mpc are implausibly small and, together with the near-exact value 69.99999, suggest a numerical artifact. The authors should report the MCMC chains, a check with H0 fixed, or a marginalized likelihood for H0.
[IV.C, Fig. 7] The slow-roll parameters are evaluated in the limit z→−1, which is the far future in this redshift coordinate, not the early-universe inflationary regime. The statement that the model 'solves the horizon and flatness problems' is therefore unsupported by the shown behavior of ϵ1 and ϵ2.
[IV, Table III] The quintessence interval is written as −1/3>ω>−1, which is reversed; it should be −1<ω<−1/3. The notation ω>>1 should be ω≫1.
[Throughout] There are numerous typographical and phrasing errors, e.g., 'P antheon', 'alikeness', 'the EoS traverses from positive to negative, which tends to −1', and the erratic spacing in 'f (Q, T)'. A careful editorial pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the derivation is a transparently parameterized fit built on an explicitly stated jerk ansatz, not a hidden reduction of its own outputs.

full rationale

The paper's derivation chain is openly parametric: the f(Q,T) field equations are used to express the density and pressure in terms of H and H-dot, after which an explicit kinematic assumption j(z)=1+q(z)+q^2(z)/2 is introduced to solve for q(z) and H(z). The subsequent quantities (transition redshift, equation of state, energy conditions, quintessence/ekpyrotic labels) are algebraic consequences of that assumed form and of the fitted parameters, so they are conditional on the ansatz rather than independent first-principles predictions. That is a modeling limitation, but it is not circularity by construction, because the assumed jerk is not defined in terms of the reported outputs and the reported outputs are not used as inputs to define the model. The h0-tension discussion reports a fitted Hubble constant and compares it with external estimates; fitting a parameter and comparing it with external values is a statistical statement, not a prediction equivalent to its inputs. The skeptic's claimed exact cancellation of H0 in the Pantheon likelihood is also not exhibited by the printed equations: with D_L proportional to H0^{-1} and mu0 containing an additional -5 log10 H0, the H0 terms do not cancel in Eqs. (24)-(27) as written. No load-bearing premise rests on a self-citation by the authors, and no uniqueness or existence theorem is imported from their previous work. Accordingly, no circular step satisfying the evidentiary standard can be identified.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The model's cosmic expansion is set by the ad hoc jerk ansatz and the free constants α and H0; the f(Q,T) parameters ζ and γ are fixed by hand and do not enter H(z). No new physical entities are introduced.

free parameters (5)

α (integration constant in q(z)) = 0.307 ± 0.011 (OHD), 0.49999 ± 0.000097 (Pantheon), 0.99999 ± 0.00011 (joint)
Arbitrary constant from solving the assumed jerk equation; fit to data.
H0 (present Hubble constant) = 70.03 ± 0.77 (OHD), 69.99998 ± 0.0001 (Pantheon), 69.99999 ± 0.0001 (joint)
Present expansion rate; fit to data, though Pantheon constraint is statistically suspect.
ζ (coefficient of Q²) = -1.82
Chosen by hand for plotting ρ, p, ω; not constrained by data.
γ (coefficient of T) = -0.9
Chosen by hand for plotting; not constrained by data.
β (normalization constant) = H0 / (e^{2√6α}+1)^{2/3}
Not independent; defined in terms of α and H0 in Eq. (21).

assumptions (5)

standard math f(Q,T) field equations from Xu et al. [81] are correct and applicable
The paper uses the field equations from ref [81] without re-derivation.
domain assumption Flat FLRW metric and perfect fluid matter description
Standard cosmological assumptions, stated in Section II.
ad hoc to paper The jerk parameter satisfies j(z)=e^{q(z)} and is approximated by 1+q+q²/2
This ansatz is not derived from the theory; it fully determines H(z) and all derived cosmic behavior.
ad hoc to paper n=2, m=1 chosen in f(Q,T)=ζQ^n+γT^m
Motivated by refs [81,82], but not derived from first principles.
ad hoc to paper ζ<0 and γ are arbitrary constants with no constraints from theory or data
Fixed to ζ=-1.82, γ=-0.9 for the plots of ρ, p, and ω.

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Cite this review

Pith. "Pith review of Cosmic reverberations on a constrained $ f(Q,T) $-model of the Universe." pith.science (2026). https://pith.science/paper/NNMYMTM6

@misc{pith2026241212210,
  author       = {Pith},
  title        = {Pith review of: Cosmic reverberations on a constrained $ f(Q,T) $-model of the Universe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NNMYMTM6}},
  note         = {Machine review of arXiv:2412.12210}
}

abstract

In this paper, we construct an isotropic cosmological model in the $ f(Q, T) $ theory of gravity in the frame of a flat FLRW spacetime being $ Q $ the non-metricity tensor and $ T $ the trace of the energy-momentum tensor. The gravity function is taken to be a quadratic equation, $ f(Q, T)=\zeta Q^2 + \gamma T $, where $ \zeta<0 $ and $ \gamma $ are the arbitrary constants. We constrain the model parameters $ \alpha $ and $ H_0 $ using the recent observational datasets: the Hubble dataset (OHD), the $ Pantheon $ dataset of $ 1048 $ points, and the joint dataset (OHD + $ Pantheon $). The universe model transitions from an early deceleration state to an acceleration in late times. This model also provides the ekpyrotic phase of the universe on the redshift $ z>12.32 $. In this model, the Big Bang is described as a collision of branes, and thus, the Big Bang is not the beginning of time. Before the Big Bang, there is an ekpyrotic phase with the equation of state $ \omega >> 1 $. In late times, the undeviating Hubble measurements reduce the $ H_0 $ tension in the reconstructed $ f(Q, T) $ function. Additionally, we study various physical parameters of the model. Finally, our model describes a quintessence dark energy model at later times.

Figures

Figures reproduced from arXiv: 2412.12210 by the authors.

**Figure 2.** FIG. 2: The alikeness of our model with ΛCDM for OHD, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** FIG. 3: The evolution of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4: The evolution of the [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: FIG. 5: The variations of the NEC, SEC, and DEC, respectively. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: FIG. 6: The evolution of the [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: FIG. 7: The evolution of the [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: FIG. 8: The recent approximations of the [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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The inflaton rolls slowly down the potential, meaning the velocity of the field ˙ϕ is small, being ϕ the scalar field corresponding to the potential V (ϕ)

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