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arxiv: 2604.21151 · v1 · submitted 2026-04-22 · 🌀 gr-qc

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The f(Q, T) gravity and affine EoS: observational aspects

Romanshu Garg , G. P. Singh
Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:10 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(Q,T) gravityaffine equation of statecosmic expansionobservational constraintsuniverse ageBayesian fittingcosmographic parameters
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The pith

A linear f(Q,T) gravity model with affine equation of state produces a present universe age consistent with Planck results within 1σ when fit to cosmic chronometer, Pantheon+SH0ES and DESI BAO data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether a particular extension of symmetric teleparallel gravity can reproduce the observed expansion of the universe. It adopts the linear coupling f(Q,T) = Q + βT and pairs it with an affine equation of state for the matter content. Parameters are constrained through Bayesian fitting to three independent datasets that trace cosmic expansion at different redshifts. The resulting model yields an age of the universe that lies inside the 1σ interval reported by Planck. Additional derived quantities such as energy density, pressure, equation of state and cosmographic parameters are examined to map the evolutionary history.

Core claim

Within the f(Q,T) framework using the linear form f(Q,T) = Q + βT and the affine equation of state, χ² minimization against Cosmic Chronometer, Pantheon+SH0ES and DESI BAO observations constrains the free parameter β and the present-day Hubble value so that the computed age of the universe today falls within 1σ of the Planck measurement. The same parameter set produces expressions for energy density, pressure, the equation of state parameter and the cosmographic quantities that describe a smooth transition from early deceleration to late-time acceleration.

What carries the argument

The linear function f(Q,T) = Q + βT together with the affine equation of state, which together modify the Friedmann equations and determine the evolution of the scale factor.

If this is right

  • The model parameters β and H0 are bounded by the combination of cosmic chronometer, supernova and BAO measurements.
  • Energy density decreases and pressure becomes negative at late times, reproducing the observed acceleration.
  • The equation of state parameter crosses from positive to negative values, tracing the expected transition from matter domination to acceleration.
  • Cosmographic parameters such as the deceleration parameter change sign at a redshift consistent with supernova data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework may serve as an alternative to explicit dark-energy components by encoding acceleration in the gravitational sector.
  • Extending the same affine equation of state to higher-redshift probes such as CMB or gravitational-wave standard sirens could test the model further.
  • If the age consistency holds under additional datasets, it would suggest that the affine form captures effective late-time behavior without introducing extra degrees of freedom.

Load-bearing premise

The linear form f(Q,T) = Q + βT together with the affine equation of state is assumed to be an adequate description of the matter sector and gravitational dynamics across the redshift range probed by the data.

What would settle it

A future determination of the present age of the universe, using the same datasets and the same linear model, that falls outside the 1σ Planck interval would falsify the reported consistency.

Figures

Figures reproduced from arXiv: 2604.21151 by G. P. Singh, Romanshu Garg.

Figure 1
Figure 1. Figure 1: In comparison to the ΛCDM model, the best fit Hubble parameter versus z. In this context, Hth signify the theoretical values of the Hubble parameter, Hobs(zi) is used to signify the observed values. The notation σH is assigned to express the standard deviation of each Hobs(zi) observed value. The best-fit Hubble parameter curve derived from equations (16) is displayed in figure (1) along with the error bar… view at source ↗
Figure 2
Figure 2. Figure 2: Marginalized 1D and 2D contour map with median values of H0, m and n using Joint data set. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: ωe f f versus z. early cosmic times. The cosmic evolution is currently dominated by quintessence like dark energy −1 < ω < −1 3 , ultimately approaching the ΛCDM scenario ω = −1 as z → −1. The smooth evolution of ωe f f suggests that the model successfully describe the transition from decelerated to accelerated expansion and may provide insights into the dynamical nature of dark energy. The model provides … view at source ↗
Figure 5
Figure 5. Figure 5: The Jerk parameter versus z. Figure (5) illustrated the jerk parameter’s behavior corresponding to the median values of model parame￾ters. In the figure (5), At higher redshift values (z >> 1) corresponding to the early Universe, the jerk parameter tends to approach a nearly constant value for both data sets. This behavior reflects the dominance of matter in the cosmic energy budget in the early universe a… view at source ↗
read the original abstract

In this paper, we investigate the cosmic expansion scenarios within the framework of $f(Q,T)$ gravity by using the affine equation of state (EoS) parameter. Specifically, we consider the linear form $f(Q,T)=Q+\beta T$, where $\beta$ is a free model parameter. We use Bayesian statistical methods, specifically the $\chi^2$ minimization technique to constrain the model parameters using Cosmic Chronometer (CC), Pantheon+SH0ES and DESI BAO data. We further analyze the characteristics of the derived cosmological model. A comprehensive study of energy density, pressure, equation of state parameter and cosmographic parameters are carried out to understand the evolution of the Universe in this model. The determination of present age of the universe for this model is within $1\sigma$ with Planck results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript investigates cosmic expansion in f(Q,T) gravity with the linear ansatz f(Q,T)=Q+βT and an affine equation of state. Model parameters are constrained via χ² minimization on Cosmic Chronometer, Pantheon+SH0ES, and DESI BAO data. The authors examine the evolution of energy density, pressure, equation of state, and cosmographic parameters, and report that the present age of the universe is consistent within 1σ with Planck results.

Significance. If the high-redshift extrapolation holds, the work offers a one-parameter modified-gravity model that accommodates current low-to-moderate redshift data while yielding an age compatible with CMB measurements. The multi-dataset fit is a modest strength, but the result's significance is limited by the lack of demonstrated early-universe consistency.

major comments (1)
  1. [Abstract] Abstract and age-determination section: the claim that t_0 lies within 1σ of Planck rests on t_0 = ∫_0^∞ dz/[(1+z)H(z)] with H(z) obtained from the f(Q,T) field equations under the affine EoS. The data sets constrain only z ≲ 2.5; the manuscript provides no check that the modified continuity equation and affine form (p = α(ρ − ρ_0)) remain physical or recover standard asymptotics at z ≫ 1, rendering the numerical age and its error budget non-robust.
minor comments (2)
  1. [Abstract] The abstract states 'Bayesian statistical methods, specifically the χ² minimization technique'; χ² minimization is frequentist unless explicit priors are introduced—clarify the statistical framework and any priors used.
  2. [Data analysis] No explicit discussion of covariance matrices or cross-dataset systematics when combining CC, Pantheon+SH0ES, and DESI BAO appears in the data-analysis description.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The concern regarding the robustness of the present-age determination is well-taken, and we will revise the paper to include explicit verification of the high-redshift asymptotics.

read point-by-point responses

  1. Referee: [Abstract] Abstract and age-determination section: the claim that t_0 lies within 1σ of Planck rests on t_0 = ∫_0^∞ dz/[(1+z)H(z)] with H(z) obtained from the f(Q,T) field equations under the affine EoS. The data sets constrain only z ≲ 2.5; the manuscript provides no check that the modified continuity equation and affine form (p = α(ρ − ρ_0)) remain physical or recover standard asymptotics at z ≫ 1, rendering the numerical age and its error budget non-robust.

    Authors: We agree that the observational constraints are limited to z ≲ 2.5 and that an explicit check of the high-redshift regime is necessary to support the age integral. In the revised manuscript we will add a dedicated subsection (and associated figures) that derives the asymptotic behavior of ρ(z), p(z), and the effective equation-of-state parameter as z → ∞. We will demonstrate that the modified continuity equation together with the affine EoS yields a physically acceptable power-law scaling for the energy density at early times, with no divergences or unphysical negative densities, and that the Hubble parameter remains positive and monotonically increasing. This will confirm that the improper integral for t_0 converges and that the reported 1σ consistency with Planck is not an artifact of uncontrolled extrapolation. We view this addition as a necessary strengthening of the work. revision: yes

Circularity Check

1 steps flagged

Reported universe age is computed from parameters fitted to CC/Pantheon+/DESI data; agreement with Planck is not an independent check

specific steps
  1. fitted input called prediction [Abstract (final sentence) and results section on age determination]
    "The determination of present age of the universe for this model is within 1σ with Planck results."

    The age is obtained by direct integration of the Hubble function whose parameters were constrained by the same late-time datasets (CC, Pantheon+SH0ES, DESI BAO). The reported 1σ overlap with Planck is therefore a post-fit derived quantity, not an independent test of the model at high redshift.

full rationale

The paper assumes the linear form f(Q,T)=Q+βT together with an affine EoS, derives H(z) from the modified field equations, fits the free parameters to Cosmic Chronometer, Pantheon+SH0ES and DESI BAO data via χ², then evaluates t0=∫dz/[(1+z)H(z)] from z=0 to ∞ and reports that this t0 lies within 1σ of the Planck value. Because the integral is evaluated on the same fitted H(z) (with the model assumed to hold at all redshifts), the numerical agreement is a direct consequence of the fit rather than an out-of-sample prediction or first-principles result. No other load-bearing steps reduce to self-definition or self-citation chains; the central derivation of the background equations is independent of the age claim. This produces partial circularity (score 6) but does not render the entire analysis tautological.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the ad-hoc choice of linear f(Q,T) and affine EoS, plus the standard FLRW assumption; β is the sole free parameter fitted to data.

free parameters (1)
  • β
    Free parameter in the linear f(Q,T)=Q+βT model, determined by χ² fit to the three data sets.
axioms (2)
  • domain assumption FLRW metric describes the background cosmology in f(Q,T) gravity
    Invoked to derive the modified Friedmann equations.
  • ad hoc to paper Affine equation of state closes the system for matter
    Specific functional choice introduced to obtain analytic or numerical solutions.

pith-pipeline@v0.9.0 · 5435 in / 1260 out tokens · 51036 ms · 2026-05-09T23:10:00.558835+00:00 · methodology

discussion (0)

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Reference graph

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