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arxiv: 2604.17017 · v1 · submitted 2026-04-18 · 🌀 gr-qc

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Transiently accelerating cosmological model with Gong-Zhang parametrization in f(T) teleparallel gravity

G. P. Singh, Khomesh R. Patle

Pith reviewed 2026-05-10 06:29 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(T) gravityteleparallel gravitydark energyGong-Zhang parametrizationtransient accelerationdeceleration parameterquintessencecosmological models
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The pith

A power-law f(T) model with Gong-Zhang dark energy parametrization produces transient cosmic acceleration followed by future deceleration.

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

The paper constructs an f(T) teleparallel gravity model using the specific power-law form f(T) = α(-T)^n together with the Gong-Zhang parametrization of the dark energy equation of state. It derives the Hubble expansion rate as a function of redshift and then examines the deceleration parameter, energy density, pressure, and equation of state evolution. The central result is that the present-day acceleration is only temporary and the universe will decelerate again at later times while the dark energy component exhibits quintessence-like behavior today. The model is confronted with cosmic chronometer and Pantheon supernova data via Bayesian fitting, and it is shown to satisfy the generalized second law of thermodynamics.

Core claim

By adopting the power-law ansatz f(T) = α(-T)^n in conjunction with the Gong-Zhang parametrization of the dark energy equation of state, the derived Hubble parameter yields a deceleration parameter that changes sign twice: the universe is currently accelerating but will enter a decelerating phase in the future. Both geometrical and dynamical diagnostics indicate quintessence-like dark energy at the present epoch, while the model remains thermodynamically viable according to the generalized second law and produces an age of the universe consistent with observations.

What carries the argument

The power-law form f(T) = α(-T)^n in f(T) teleparallel gravity, combined with the Gong-Zhang parametrization of the dark energy equation of state, which together determine the redshift-dependent Hubble rate and all derived cosmological quantities.

If this is right

  • The deceleration parameter crosses zero twice, marking a finite period of acceleration between two decelerating eras.
  • The dark energy equation of state remains greater than -1 today, consistent with quintessence rather than phantom behavior.
  • Energy conditions for the dark energy component are satisfied in a manner compatible with observed expansion history.
  • The model satisfies the generalized second law of thermodynamics at all times.

Where Pith is reading between the lines

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

  • If the transient acceleration result holds, long-term cosmological forecasts would need to replace a perpetual de Sitter phase with an eventual return to matter-like deceleration.
  • The same functional forms could be applied to other modified gravity theories to test whether transient acceleration is generic or specific to this f(T) choice.
  • High-redshift surveys that tightly constrain the equation of state beyond z ≈ 2 would directly test whether the Gong-Zhang parametrization remains accurate far from the present epoch.

Load-bearing premise

The power-law ansatz for f(T) and the Gong-Zhang parametrization remain valid over the entire redshift range, including the extrapolated future.

What would settle it

Future measurements of the deceleration parameter or dark energy equation of state at low redshifts (z < 0) that show continued acceleration rather than a return to deceleration would rule out the model's central prediction.

Figures

Figures reproduced from arXiv: 2604.17017 by G. P. Singh, Khomesh R. Patle.

Figure 1
Figure 1. Figure 1: The best-fit H(z) curve for the proposed model is compared with the ΛCDM model. parameterized form of the Hubble parameter in equation (24), are constrained using the cosmic chronome￾ter (CC) dataset along with the combined (CC+Pantheon) dataset. The estimation of these parameters is performed by minimizing the χ 2 function, together with the Markov chain Monte Carlo (MCMC) sampling technique, implemented … view at source ↗
Figure 2
Figure 2. Figure 2: Marginalized 1D and 2D posterior contour map with median values of H0, ω0 and n using the Joint dataset. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Plot of the deceleration parameter (q) with z. 5 The physical and dynamical characteristics of the model 5.1 Analysis of deceleration parameter The deceleration parameter q is a fundamental quantity for characterizing the expansion dynamics of the universe, as it provides insight into the nature of cosmic evolution. Different values of q correspond to distinct expansion regimes: q < 0 signifies an accelera… view at source ↗
Figure 5
Figure 5. Figure 5: Plot of pressure (pDE) with z. 5.2 Observational study of energy density, pressure and equation of state parameter We examine the physical properties of key cosmological quantities, namely the energy density and pressure. For the constrained model parameters, the energy density remains positive throughout the cosmic expan￾sion, while the pressure exhibits negative values, driving the accelerated expansion … view at source ↗
Figure 6
Figure 6. Figure 6: Plot of EoS parameter (ωDE) with z. The graphical evolution of the EoS parameter for the proposed model is illustrated in Fig. (6). The present-day values at z = 0 are found to be ωDE = −0.769 for the CC dataset and ωDE = −0.843 for the joint dataset. These values indicate that the model exhibits a quintessence-like behavior of DE at the current epoch for both datasets. The evolution of ωDE further suggest… view at source ↗
Figure 7
Figure 7. Figure 7: The components of energy conditions with [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Plot of s and r plane. • In the Chaplygin gas (CG) model, the parameters typically satisfy (r > 1, s < 0). • The standard ΛCDM model is represented by r = 1 and s = 0. • For Quintessence model, one generally finds (r < 1, s > 0). • Holographic dark energy (HDE) model, (r = 1, s = 2 3 ). • For Standard cold dark matter (SCDM), one may have (r = 1, s = 1). The evolutionary trajectories of the proposed model … view at source ↗
Figure 9
Figure 9. Figure 9: Plot of Om(z) diagnostics with z. powerful diagnostic tool for exploring dark energy dynamics, effectively delineating regions corresponding to accelerated cosmic expansion. This methodology, first proposed by Caldwell and Linder [98] for quintessence scalar fields, offers a systematic approach for categorizing dark energy models according to their evolutionary trajectories. Two characteristic behaviors ar… view at source ↗
Figure 10
Figure 10. Figure 10: Plot of (ωDE −ω ′ DE) plane. ity of this law has also been examined in the framework of f(T) teleparallel gravity in earlier studies [33, 60], highlighting its significance in modified gravitational scenarios. In this work, we employ the Gong-Zhang parametrization of the DE EoS parameter within the framework of f(T) teleparallel gravity. It is therefore of considerable interest to examine whether the prop… view at source ↗
Figure 11
Figure 11. Figure 11: Plot of S˙ tot with z. where the subscript ‘t’ denotes the total quantity and Vh = 4 3 πR 3 h represents the volume enclosed by the ap￾parent horizon. Therefore, the rate of change of entropy associated with the fluid inside the horizon can be written as S˙ in = (ρt + pt)V˙ h +ρ˙tVh Tin . (42) Under the assumption of thermal equilibrium between the cosmic fluid and the horizon, the temperature of the flui… view at source ↗
read the original abstract

We present the cosmic expansion scenario in the framework of $f(T)$ gravity by employing a dark energy equation of state (EoS) parameter. Specifically, we proceed with the power-law form of the function $f(T) = \alpha$$(-T)^{n}$, in conjunction with the Gong-Zhang parametrization of the dark energy EoS. We derive the expansion rate in terms of the redshift for the considered model, providing deeper insights into the underlying cosmic dynamics. The model is further utilized to explore the expansion history of the universe and the evolution of several cosmological parameters. By using the Bayesian methods based on the $\chi^{2}$-minimization technique, the median values of the model parameters are determined for the cosmic chronometer (CC) and joint (CC+Pantheon) datasets. The evolution of the deceleration parameter, energy density, pressure, EoS parameter and the energy conditions for dark energy is analyzed in detail. The model captures the observed acceleration as a transient phenomenon, followed by future deceleration. Additionally, the nature of both geometrical and dynamical diagnostics robustly indicates a quintessence-like behavior at the present epoch. Finally, the thermodynamic viability of the model is confirmed through the generalized second law of thermodynamics and the estimated age of the universe further supports the model's compatibility with astronomical observations.

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

2 major / 2 minor

Summary. The manuscript presents a cosmological model in f(T) teleparallel gravity employing the power-law ansatz f(T) = α(-T)^n together with the Gong-Zhang parametrization of the dark-energy equation of state. The authors derive an analytic expression for the Hubble rate H(z), determine the free parameters (α, n, w0, w1) by χ² minimization against cosmic-chronometer and Pantheon supernova data, and then examine the redshift evolution of the deceleration parameter q(z), energy density, pressure, EoS parameter, energy conditions, and thermodynamic quantities. They conclude that the present-day acceleration is transient and will be followed by deceleration at future times, while the present epoch exhibits quintessence-like behavior; thermodynamic viability is asserted via the generalized second law.

Significance. If the transient-acceleration result survives robustness checks, the work supplies a concrete, observationally calibrated example of how a simple f(T) modification can produce a temporary accelerated phase without a cosmological constant. The combination of analytic derivation, numerical fitting to two independent datasets, and multiple geometric/dynamical diagnostics is a positive feature. The significance is nevertheless reduced by the absence of quantified uncertainties on the future q(z) sign change and by the lack of tests against alternative parametrizations that fit the same data.

major comments (2)
  1. [Results / deceleration-parameter evolution] Results section on the deceleration parameter: the central claim that acceleration is transient (q0 < 0 followed by q(z) > 0 for some z < 0) is obtained by extrapolating the fitted Gong-Zhang wDE(z) and power-law f(T) beyond the redshift range of the data (z ≲ 2). No error bands, MCMC posterior samples, or prior-variation tests are shown for the future sign change in q(z), so it is impossible to assess whether the claimed transition is robust or an artifact of the chosen functional forms.
  2. [Model construction and fitting procedure] Parameter-fitting and model-construction paragraphs: the Gong-Zhang parameters w0, w1 and the exponents n, α are determined by minimizing χ² against the identical CC + Pantheon datasets that are later used to assert the transient behavior. Because the future evolution is a direct consequence of the fitted ansatz rather than an independent prediction, the manuscript must demonstrate that the sign change in q(z) persists under equally plausible alternative parametrizations that also fit the data.
minor comments (2)
  1. [Abstract and thermodynamic analysis] The abstract states that the model is “thermodynamically viable” but does not specify which form of the generalized second law is employed or whether the entropy production rate remains positive for all future times; a brief clarification would improve readability.
  2. [Notation throughout] Notation for the Gong-Zhang parameters (w0, w1) and the f(T) exponents (n, α) should be introduced once in the model section and used consistently thereafter; occasional redefinition of symbols in later figures is distracting.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address each major comment below and outline the revisions we will make to improve the presentation and robustness of our results.

read point-by-point responses

  1. Referee: Results section on the deceleration parameter: the central claim that acceleration is transient (q0 < 0 followed by q(z) > 0 for some z < 0) is obtained by extrapolating the fitted Gong-Zhang wDE(z) and power-law f(T) beyond the redshift range of the data (z ≲ 2). No error bands, MCMC posterior samples, or prior-variation tests are shown for the future sign change in q(z), so it is impossible to assess whether the claimed transition is robust or an artifact of the chosen functional forms.

    Authors: We agree with the referee that displaying uncertainties is crucial for assessing the robustness of the future deceleration. In the revised manuscript, we will include 1σ and 2σ confidence bands on the deceleration parameter q(z) derived from the covariance matrix of the best-fit parameters obtained via χ² minimization. This will allow readers to evaluate the statistical significance of the sign change in q(z) at negative redshifts. We will also mention the limitations of extrapolation beyond the data range. revision: yes

  2. Referee: Parameter-fitting and model-construction paragraphs: the Gong-Zhang parameters w0, w1 and the exponents n, α are determined by minimizing χ² against the identical CC + Pantheon datasets that are later used to assert the transient behavior. Because the future evolution is a direct consequence of the fitted ansatz rather than an independent prediction, the manuscript must demonstrate that the sign change in q(z) persists under equally plausible alternative parametrizations that also fit the data.

    Authors: The Gong-Zhang parametrization was selected for its ability to model the dark energy EoS with a simple form that accommodates both past and future evolution. We acknowledge that the transient acceleration is specific to this choice. In the revision, we will add a paragraph in the discussion section comparing briefly with the Chevallier-Polarski-Linder (CPL) parametrization using the same f(T) form, noting any differences in the predicted future behavior. However, an exhaustive test of all possible parametrizations is beyond the scope of this work, as our focus is on providing an analytic model with the Gong-Zhang form calibrated to observations. revision: partial

Circularity Check

0 steps flagged

No significant circularity; transient behavior follows from assumed forms and data fit without reduction to inputs by construction

full rationale

The paper adopts the power-law ansatz f(T) = α(-T)^n and Gong-Zhang parametrization for w_DE(z) by explicit assumption, derives H(z) from the f(T) Friedmann equation, fits the free parameters via χ² minimization to CC and Pantheon data, and then evaluates the resulting q(z) evolution. The statement that acceleration is transient (present q0 < 0 followed by future deceleration) is a direct consequence of extrapolating the fitted functional forms to z < 0, but this does not constitute a self-definitional loop, a fitted quantity renamed as prediction, or any other enumerated circular pattern. No load-bearing self-citations, uniqueness theorems, or ansatz smuggling are present. The derivation chain is self-contained given the stated assumptions and does not reduce any claimed result to equivalence with its inputs by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The model rests on the standard FLRW metric, the teleparallel equivalent of general relativity, and the assumption that the Gong-Zhang parametrization plus power-law f(T) together constitute a complete effective description from z=0 to the future. No new particles or forces are postulated.

free parameters (3)
  • α
    Amplitude of the power-law f(T) term, fitted to data.
  • n
    Exponent of the power-law f(T) term, fitted to data.
  • w0, w1 (Gong-Zhang parameters)
    Two parameters in the dark-energy equation-of-state parametrization, fitted to data.
axioms (2)
  • standard math The universe is described by a flat FLRW metric with torsion scalar T = -6H².
    Invoked when writing the modified Friedmann equations in f(T) gravity.
  • domain assumption The Gong-Zhang parametrization w(z) = w0 + w1 z/(1+z) remains valid at all redshifts.
    Used to close the system and extrapolate to future deceleration.

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Reference graph

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