Constraining $f(Q,\mathcal{L}_{m})$ gravity with redshift-dependent pressure: Insights from observational probes

Amit Samaddar; S. Surendra Singh

Constraining $f(Q,\mathcal{L}_{m})$ gravity with redshift-dependent pressure: Insights from observational probes

T0 review · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A minimal f(Q,L_m) gravity model with redshift-dependent pressure is claimed to fit combined Hubble, BAO, and supernova data and to unify inflation with late-time acceleration.

desk verdict Load-bearing algebra error in the continuity solution invalidates the claimed acceleration and inflation results. read the letter →

arxiv 2508.04738 v1 pith:XKH2FDYV submitted 2025-08-05 gr-qc hep-th

Amit Samaddar , S. Surendra Singh This is my paper

classification gr-qchep-th MSC 83D0583F05

keywords f(QLm)gravitynonmetricityscalarredshift-dependentpressureMarkovchainMonteCarlodecelerationparameterenergyconditionsslow-rollinflationcosmologicalconstraints

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 sets out to show that a minimal linear form of $f(Q,\mathcal{L}_{m})$ gravity with $f=-Q+2\mathcal{L}_{m}+\gamma$, together with the pressure parametrization $p(z)=\alpha+\beta z/(1+z)$, can account for late-time cosmic acceleration while fitting the same kinds of data used to constrain standard cosmology. Combining 46 Hubble points, 15 BAO points, and 1701 Type Ia supernovae, an MCMC fit gives $H_{0}=67.95\pm0.75$ km/s/Mpc and predicts a deceleration-to-acceleration transition at $z_{\mathrm{tr}}\approx0.493$, with present values $q_{0}=-0.255$ and $\omega_{0}=-0.9001$. The paper also claims the model satisfies the null and dominant energy conditions, violates the strong energy condition at late times, and admits a smooth slow-roll inflationary phase. If these claims hold, one four-parameter functional form for $f(Q,\mathcal{L}_{m})$ would bridge early-Universe inflation and the present accelerated expansion.

What carries the argument

The load-bearing object is the linear action $f(Q,\mathcal{L}_{m})=-Q+2\mathcal{L}_{m}+\gamma$, with $Q=6H^{2}$ the non-metricity scalar in a flat FLRW universe. It is paired with the pressure law $p(z)=\alpha+\beta z/(1+z)$, which runs from $\alpha+\beta$ at high redshift to $\alpha$ today. The paper uses the standard fluid conservation equation to convert this pressure law into an explicit $\rho(z)$ and hence $H(z)$, then constrains the four parameters with a joint MCMC likelihood. The deceleration parameter and slow-roll parameters $\epsilon_{1},\epsilon_{2}$ are computed from the fitted $H(z)$ to diagnose the expansion and inflation history.

What would settle it

Substitute the paper's Eq. (20) for $\rho(z)$ and Eq. (18) for $p(z)$ into Eq. (19): the left-hand side becomes $3z[(\alpha+\beta)-\beta/(1+z)]$, which is not zero for the best-fit values. Recomputing $\rho(z)$ by direct integration and rerunning the MCMC fit would settle whether the reported $z_{\mathrm{tr}}$, $q_{0}$, and $\omega_{0}$ survive.

Watch

Extended reading notes

Core claim

The paper's central claim is that $f(Q,\mathcal{L}_{m})=-Q+2\mathcal{L}_{m}+\gamma$ with $\mathcal{L}_{m}=\rho$ and $p(z)=\alpha+\beta z/(1+z)$ is a viable unified cosmology. Its modified Friedmann equations give an $H(z)$ that, fit to cosmic chronometer, BAO, and supernova data, yields $H_{0}=67.9476^{+0.7534}_{-0.7523}$ km/s/Mpc, with $\alpha,\beta,\gamma$ consistent with zero at $1\sigma$. The fit predicts a deceleration-to-acceleration transition at $z_{\mathrm{tr}}\approx0.493$, present $q_{0}=-0.255$ and $\omega_{0}=-0.9001$, NEC and DEC satisfaction, SEC violation at low redshift, and $\epsilon_{1}$ crossing unity near $z=-0.48$ to end inflation. These results are interpreted as unify

Load-bearing premise

In Section 3 the paper assumes the standard FLRW conservation law $\dot{\rho}+3H(\rho+p)=0$ holds for this $f(Q,\mathcal{L}_{m})$ model and integrates it to obtain the $\rho(z)$ used in every later result; if that conservation law is not actually forced by the theory, the predicted $H(z)$, deceleration, equation of state, energy conditions, and slow-roll parameters all shift.

Editorial extensions

If this is right

If the model is right, a single four-parameter framework reproduces the measured expansion history, with $H_0$ consistent with both CMB and local distance-ladder estimates.
The predicted transition redshift $z_{\mathrm{tr}}\approx0.493$ and $q_0\approx-0.255$ give a concrete epoch for the switch from matter-dominated deceleration to accelerated expansion.
The equation of state stays negative at all redshifts and tends to $-1$, so the model behaves as quintessence approaching a cosmological constant without crossing to phantom.
Satisfaction of NEC and DEC with SEC violation at late times locates the model within the standard energy-condition pattern expected of accelerated expansion.
The slow-roll analysis gives inflation an end at $z\approx-0.48$, so the same $\gamma$ term can seed both the early accelerated phase and the late one.

Reading between the lines

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

My inference: the reported posteriors put $\alpha$, $\beta$, and $\gamma$ all within $1\sigma$ of zero, so the data do not yet distinguish this model from $\Lambda$CDM; the unification claim rests on kinematic features of the best fit rather than a detected non-metricity signal.
My inference: direct substitution in Eqs. (19)-(20) leaves the continuity residual $3z[(\alpha+\beta)-\beta/(1+z)]$, which is nonzero for the best-fit parameters; if this is correct, the derived $\rho(z)$ and every quantity built on it need to be recomputed from the theory's own conservation equation.
My inference: a direct extension would be to re-run the MCMC with $\rho(z)$ obtained from Eq. (11) rather than the FLRW continuity equation and compare the resulting $z_{\mathrm{tr}}$, $q_{0}$, and $H_{0}$.

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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

The paper has a load-bearing algebra error that sinks the central claim. Equation (20) is not a solution of the continuity equation (19) for the chosen p(z); substituting gives a residual 3z[(α+β)−β/(1+z)], which does not vanish for the reported parameters. All the derived H(z), q, ω, energy conditions, and slow-roll parameters inherit the error. The abstract's q0=−0.255 and ω0=−0.9001 are not what the model with the fitted parameters predicts: with α≈β≈γ≈0, Eq. (32) gives q0≈0.5, a decelerating EdS universe.

To give credit where it is earned, the combination is new: the known linear f(Q,L_m)=−Q+2L_m+γ model is joined with the Zhang et al. pressure parametrization p(z)=α+βz/(1+z), and the fit uses up-to-date data including DESI DR2 BAO and Pantheon+. The MCMC setup is standard, with emcee and clear priors; no code or data are provided, but the statistical machinery is not the main issue.

The soft spots are serious. First, the continuity error is not a theory-specific loophole; the standard conservation law is the appropriate one here because f_Lm is constant and the hypermomentum vanishes. Second, the figures for ρ, p, ω, energy conditions, and slow-roll are labelled 'with γ=0.5' (Figures 4, 5, 6, 7), which is not the MCMC best fit. So the shown phenomenology—the negative pressure, the EoS tending to −1, the SEC violation—is not the phenomenology of the fitted model. Third, the slow-roll discussion is purely kinematic and places the end of inflation at z=−0.48, which is in the future; that is not a sensible inflationary statement. Fourth, the abstract's claim of unifying inflation and late-time acceleration is unsupported by any early-universe data or by a dynamical mechanism.

Who is this for? A reader tracking f(Q,L_m) parameter constraints might skim it, but the results are not reliable. The internal inconsistency between the best-fit parameters (all consistent with zero) and the reported q0 and ω0 is a fundamental flaw, not a matter of taste.

I would not send this to referees in its current form. The central derivation is broken, and the paper contradicts its own equations. If the authors correct the continuity solution, redo the fit, and remove the unsupported inflation extrapolation, a revised version could be worth a referee's time, but that would be a major rewrite.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the derivation chain is a standard fit-and-extrapolate exercise; its failures are mathematical (continuity equation not satisfied) and internal inconsistency, not circularity. Score 1 for loose 'prediction' language and non-load-bearing self-citations.

full rationale

The paper's derivation chain is: choose f(Q,L_m)=-Q+2L_m+γ (Eq. 17); choose pressure parametrization p(z)=α+βz/(1+z) (Eq. 18); integrate the standard FLRW continuity equation (19) to obtain ρ(z) (Eq. 20); substitute into the modified Friedmann equation (15) to get H(z) (Eqs. 21-22); then compute q(z) (Eq. 32), ω(z) (Eq. 35), energy conditions (Eqs. 36-38), and slow-roll parameters (Eqs. 40-41) from H, ρ, p. The derived quantities z_tr, q0, ω0 are deterministic functions of the fitted parameters H0, α, β, γ. That makes them postdictions, not independent predictions, but it is not circular: the parameters are constrained by external data (CC, BAO, SNe), and the derived quantities are not themselves fit targets. The paper reports q0=-0.255 and ω0=-0.9001 in the abstract, but substituting the quoted best-fit parameters (α≈-0.0002, β≈-0.0001, γ≈0.0002, H0≈67.95) into Eq. (32) gives q0≈0.5, and Eq. (35) gives ω0≈0, so the published numbers are internally inconsistent with the stated fit; the figures appear to use γ=0.5. Additionally, direct substitution shows Eq. (20) is not a solution of the continuity equation (19): the residual is 3z[(α+β)-β/(1+z)], which vanishes only for special parameter relations. These are serious mathematical/internal-consistency defects, but they are not circularity, because the 'predictions' do not reduce to the inputs by construction; they are simply invalid or misreported. The paper's citations of prior work by the same authors ([10,20,24,25,26,33]) are general references to the f(Q,L_m) framework and parametrization literature and are not load-bearing for the specific derivation, which rests on external citations [27,31]. No uniqueness theorem or ansatz is smuggled in via self-citation. Overall circularity score: 1/10, reflecting only the loose use of 'prediction' for postdicted quantities.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles or forces. Its free parameters are the four MCMC-fitted constants, plus the ad hoc pressure ansatz and the L_m=rho and conservation assumptions that are not independently established.

free parameters (4)

H0 = 67.9476 km/s/Mpc
Hubble constant fit to combined Hubble, BAO, and Pantheon+ data.
alpha = -0.0002
Constant term in the pressure parametrization p(z)=alpha+beta z/(1+z), fitted by MCMC.
beta = -0.0001
Redshift-dependent coefficient in the pressure parametrization, fitted by MCMC.
gamma = 0.0002
Effective cosmological-constant-like term in f(Q,L_m)=-Q+2L_m+gamma, fitted by MCMC.

assumptions (4)

domain assumption Standard FLRW energy-momentum conservation \dot\rho+3H(\rho+p)=0 is assumed to hold in f(Q,L_m) gravity
Invoked in Section 3 (Eq. 19) despite the theory's non-conservation equation (Eq. 11) allowing B_nu != 0; no proof that B_nu vanishes for the chosen f.
ad hoc to paper The matter Lagrangian is chosen as L_m = rho
Section 3; this choice is standard in many papers but is a modeling assumption that affects the Friedmann equations.
ad hoc to paper The pressure parametrization p(z)=alpha+beta z/(1+z) is taken as a phenomenological input
Section 3, Eq. (18), from ref [31]; not derived from the theory.
ad hoc to paper Slow-roll parameters epsilon1, epsilon2 defined via H are interpreted as inflation even without a scalar field or potential
Section 7, Eqs. (39)-(41); no inflationary mechanism is provided.

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Cite this review

Pith. "Pith review of Constraining $f(Q,\mathcal{L}_{m})$ gravity with redshift-dependent pressure: Insights from observational probes." pith.science (2026). https://pith.science/paper/XKH2FDYV

@misc{pith2026250804738,
  author       = {Pith},
  title        = {Pith review of: Constraining $f(Q,\mathcalL_m)$ gravity with redshift-dependent pressure: Insights from observational probes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XKH2FDYV}},
  note         = {Machine review of arXiv:2508.04738}
}

abstract

We explore the late time cosmological dynamics of the Universe within the framework of $f(Q,\mathcal{L}_{m})$ gravity by considering the specific form $f(Q, \mathcal{L}_m)=-Q+2\mathcal{L}_m+\gamma$. To describe the cosmic pressure evolution, a redshift dependent parametrization of $p(z)=\alpha+\frac{\beta z}{1+z}$ is introduced. MCMC analysis is performed using a combined datasets from Hubble ($46$ points), BAO ($15$ points including DESI DR2) and Pantheon$+$ ($1701$ SNe Ia), the model parameters are constrained as $H_{0}=67.9476^{+0.7534}_{-0.7523}$ (km/s/Mpc), $\alpha=-0.0002^{+0.0211}_{-0.0208}$, $\beta=-0.0001^{+0.0410}_{-0.0404}$ and $\gamma=0.0002^{+0.0599}_{-0.0602}$. The model predicts a transition from deceleration to acceleration at $z_{tr} \approx 0.493$ with present values $q_{0}=-0.255$ and $\omega_{0}=-0.9001$. The evolution of energy density and pressure aligns with observational expectations. An analysis of energy conditions shows that NEC and DEC are satisfied, while SEC is violated, consistent with late time acceleration. Moreover, the slow roll parameters $\epsilon_{1}$ and $\epsilon_{2}$ confirm a smooth inflationary regime. These results demonstrate the capability of the model to unify early Universe inflation with the current phase of cosmic acceleration.

Figures

Figures reproduced from arXiv: 2508.04738 by the authors.

**Figure 2.** Joint constraint contours for (H0, α, β, γ) illustrating 1σ, 2σ and 3σ confidence levels based on the combined observational datasets. 5 Cosmological parameter dynamics 5.1 Deceleration parameter The deceleration parameter q(z) is a key cosmological indicator that helps describe the nature of the Universe’s expansion dynamics. The deceleration parameter for our model is derived from the Hubble parameter H(z) provide… view at source ↗

**Figure 3.** Redshift evolution of the deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Redshift evolution of energy density and pressure for ou [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Evolution of ω(z) for our model with γ = 0.5. from ω ≈ −0.85 to ω ≈ −1 also ensures that the model remains observationally viable and consistent with constraints from Planck 2018 and SNe Ia datasets. 6 Energy conditions analysis This section focuses on evaluating the s…

**Figure 6.** Figure 6: Evolution of energy condition expressions with redshift. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: Evolution of the slow-roll parameters ǫ1(z) and ǫ2(z) for the proposed f(Q,Lm) model [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Observationally Constrained Cosmological model in $f(Q,\mathcal{L}_{m})$ Gravity with $H(z)$ parameterization
gr-qc 2026-07 conditional novelty 3.0 of 10

An f(Q, L_m) gravity model with a parameterized H(z) fits observational data, yielding a transition redshift z_t ≈ 0.643 and cosmic age 13.724 Gyr, consistent with ΛCDM.

Reference graph

Works this paper leans on

45 extracted references · 33 canonical work pages · cited by 1 Pith paper

[1]

Riess, et al., Astron.J

Adam G. Riess, et al., Astron.J. 116:1009-1038, 1998

work page 1998
[2]

Perlmutter et al., The Astrophys

S. Perlmutter et al., The Astrophys. Journ. 517, 565 (1999)

work page 1999
[3]

Planck Collaboration, Aghanim, N., et al., Astronomy & Astrophysic s, 641, A6 (2020)

work page 2020
[4]

Alam, et al., Phys

S. Alam, et al., Phys. Rev. D 103, 083533 (2021)

work page 2021
[5]

Steven Weinberg, Rev. Mod. Phys. 61, 1, 1989. 13

work page 1989
[6]

S. M. Carroll, Living Rev. Rel., 4, 1, (2001)

work page 2001
[7]

Verde, T

L. Verde, T. Treu, A. G. Riess, Nat Astron 3, 891–895 (2019)

work page 2019
[8]

T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010)

2010

Show all 45 references

[9]

Nojiri and S

S. Nojiri and S. D. Odintsov, Phys. Rept. 505, 59, 144 (2011)

2011
[10]

Scr., 99, 035219 (2024)

Amit Samaddar and Surendra Sanasam, Phys. Scr., 99, 035219 (2024)

2024
[11]

Nojiri and S

S. Nojiri and S. D. Odintsov, Phys. Lett. B 631, 1 (2005)

2005
[12]

De Felice and S

A. De Felice and S. Tsujikawa, Living Rev. Relativity 13, 3 (2010)

2010
[13]

Harko et al., Phys

T. Harko et al., Phys. Rev. D 84, 024020 (2011)

2011
[14]

Bertolami, et al., Phys

O. Bertolami, et al., Phys. Rev. D 75, 104016 (2007)

2007
[15]

Jimenez, L

J.B. Jimenez, L. Heisenberg, and T. Koivisto, Phys. Rev. D 98, 044048 (2018)

2018
[16]

Jimenez et al., Phys

J.B. Jimenez et al., Phys. Rev. D 101, 103507 (2020)

2020
[17]

Myrzakulov et al., J

K. Myrzakulov et al., J. High Energy Astrophys. 44, 164-171 (2024)

2024
[18]

Myrzakulov et al., Phys

Y. Myrzakulov et al., Phys. Dark Universe 46, 101614 (2024)

2024
[19]

Myrzakulov et al., Phys

Y. Myrzakulov et al., Phys. Dark Universe 48, 101829 (2025)

2025
[20]

Samaddar and S.S

A. Samaddar and S.S. Singh, Nucl. Phys. B 1012, 116834 (2025)

2025
[21]

MICHEL CHEV ALLIER and DA VID POLARSKI, International Jou rnal of Modern Physics D, 10, 02, 213-223 (2001)

2001
[22]

E. V. Linder, Phys. Rev. Lett. 90, 091301 (2003)

2003
[23]

Sahni, A

V. Sahni, A. A. Starobinsky, Int.J.Mod.Phys.D 15, 2105-2132, (2006)

2006
[24]

Surendra Singh, Md Khurshid Alam, Int

Amit Samaddar, S. Surendra Singh, Md Khurshid Alam, Int. J. Mo d. Phys. D, Vol. 32, No. 09, 2350062 (2023)

2023
[25]

Samaddar, S

A. Samaddar, S. Surendra Singh, Physics of the Dark Universe , 47, 101792 (2025)

2025
[26]

Samaddar, S

A. Samaddar, S. Surendra Singh & M. K. Alam, Gravit. Cosmol. 30, 462–480 (2024)

2024
[27]

Hazarika et al

A. Hazarika et al. arXiv:2407.00989 (2024)

2024
[28]

Bertolami, F

O. Bertolami, F. S. N. Lobo, and J. Paramos, Phys. Rev. D, 78, 064036, (2008)

2008
[29]

N. S. Kavya, V. Venkatesha, Sanjay Mandal, P.K. Sahoo, Phys ics of the Dark Universe 38, 101126 (2022)

2022
[30]

Yue-Yue Zhao et al., Eur. Phys. J. C 72:1924 (2012)

1924
[31]

Zhang et al., Eur

Q. Zhang et al., Eur. Phys. J. C 75 (7), 300 (2015)

2015
[32]

D. F. Mackey et al., Publ. Astron. Soc. Pac., 125, 306 (2013)

2013
[33]

Surendra Singh, Journal of High Energy Ast rophysics, 48, 100404 (2025)

Amit Samaddar, S. Surendra Singh, Journal of High Energy Ast rophysics, 48, 100404 (2025)

2025
[34]

DESI collaboration, arXiv:2404.03000, 2024

2024 arXiv
[35]

Adame, et al., J

A.G. Adame, et al., J. Cosmol. Astropart. Phys. 01, 124 (2025)

2025
[36]

Adame, et al., J

A.G. Adame, et al., J. Cosmol. Astropart. Phys. 02, 021 (2025)

2025
[37]

Abdul Karim, et al., arXiv:2503.14738

M. Abdul Karim, et al., arXiv:2503.14738. 14

arXiv
[38]

Kowalski, et al., Astrophys

M. Kowalski, et al., Astrophys. J. 686, (2), 749 (2008)

2008
[39]

Amanullah, et al., Astrophys

R. Amanullah, et al., Astrophys. J. 716, (1), 712 (2010)

2010
[40]

Suzuki, et al., Astrophys

N. Suzuki, et al., Astrophys. J. 746, (1), 85 (2012)

2012
[41]

Betoule, et al., Astronomy & Astrophysics 568, A22 (2014)

M. Betoule, et al., Astronomy & Astrophysics 568, A22 (2014)

2014
[42]

Scolnic, et al., Astrophys

D.M. Scolnic, et al., Astrophys. J. 859, (2), 101 (2018)

2018
[43]

A. G. Riess, et al., Astrophys. J. Lett., 934, L7, (2022)

2022
[44]

Shiravand, S

M. Shiravand, S. Fakhry and M. Farhoudi, Phys. Dark Univ. 37, 101106 (2022)

2022
[45]

A. R. Liddle, P. Parsons and J. D. Barrow, Phys. Rev. D 50, 7222-7232 (1994). 15

1994

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Riess, et al., Astron.J

Adam G. Riess, et al., Astron.J. 116:1009-1038, 1998

work page 1998

[2] [2]

Perlmutter et al., The Astrophys

S. Perlmutter et al., The Astrophys. Journ. 517, 565 (1999)

work page 1999

[3] [3]

Planck Collaboration, Aghanim, N., et al., Astronomy & Astrophysic s, 641, A6 (2020)

work page 2020

[4] [4]

Alam, et al., Phys

S. Alam, et al., Phys. Rev. D 103, 083533 (2021)

work page 2021

[5] [5]

Steven Weinberg, Rev. Mod. Phys. 61, 1, 1989. 13

work page 1989

[6] [6]

S. M. Carroll, Living Rev. Rel., 4, 1, (2001)

work page 2001

[7] [7]

Verde, T

L. Verde, T. Treu, A. G. Riess, Nat Astron 3, 891–895 (2019)

work page 2019

[8] [8]

T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010)

2010