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arxiv: 2606.13261 · v1 · pith:CPZQEQL4new · submitted 2026-06-11 · 🌀 gr-qc

Probing cosmic dynamics in f(T) teleparallel gravity: Constraints from logarithmic and log-periodic deceleration ansatzes

Khomesh R. Patle , G. P. Singh This is my paper

Pith reviewed 2026-06-27 06:17 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(T) gravityteleparallel gravitydeceleration parameterdark energycosmological constraintscosmic chronometerslogarithmic parametrizationequation of state
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The pith

Logarithmic and log-periodic forms of the deceleration parameter in power-law f(T) gravity yield Hubble expansions that depart from Lambda CDM and favor dynamically evolving dark energy.

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

The paper tests cosmic expansion inside teleparallel gravity by taking f(T) equal to alpha times minus T to the power n and inserting two specific parametrizations of the deceleration parameter. These parametrizations produce an explicit Hubble rate as a function of redshift that is then fitted to cosmic chronometer and joint cosmic chronometer plus Pantheon data. The fits produce equation-of-state and geometrical diagnostics that move away from the constant value required by a cosmological constant. The same models keep energy conditions satisfied, remain thermodynamically consistent, and return an age of the universe inside observational bounds.

Core claim

Adopting logarithmic and log-periodic ansatzes for the deceleration parameter q(z) inside f(T) = alpha (-T)^n teleparallel gravity produces a Hubble parameter H(z) whose observational constraints show a clear departure from standard cosmological-constant behavior and therefore indicate dynamically evolving dark energy, while the models stay thermodynamically consistent and return an age compatible with observations.

What carries the argument

The logarithmic and log-periodic parametrizations of the deceleration parameter q(z) that fix the redshift dependence of the Hubble parameter and permit chi-squared constraints on the model parameters alpha and n.

If this is right

  • The equation of state parameter evolves with redshift rather than remaining fixed at -1.
  • Geometrical diagnostics confirm a departure from Lambda CDM behavior.
  • Energy density, pressure, and all standard energy conditions remain satisfied.
  • The models stay thermodynamically consistent at every epoch.
  • The derived age of the universe lies inside current observational limits.

Where Pith is reading between the lines

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

  • The same parametrizations could be inserted into other modified-gravity actions to test whether the evolving-dark-energy signal is specific to teleparallel geometry.
  • If the departure persists, it would motivate direct searches for geometric mechanisms inside the torsion scalar that could source the variation.
  • Future surveys at higher redshift could check whether the log-periodic form continues to describe the transition from deceleration to acceleration.

Load-bearing premise

The chosen logarithmic and log-periodic parametrizations of the deceleration parameter supply a physically adequate description of the expansion history across epochs.

What would settle it

A high-precision determination that the deceleration parameter follows exactly the Lambda CDM functional form at all redshifts, with no deviation in the geometrical diagnostics, would falsify the claim of dynamically evolving dark energy.

Figures

Figures reproduced from arXiv: 2606.13261 by G. P. Singh, Khomesh R. Patle.

Figure 1
Figure 1. Figure 1: For Model-1: Plot of q(z) with z. The analysis of the deceleration parameter q(z) obtained from the CC dataset and the joint dataset is presented in Figures (1) and (2), respectively. The results clearly indicate a transition of the universe from an earlier decelerating phase to the present accelerating epoch. Using the median values of the model parameters, the present-day value of the q(z) for Model-1 is… view at source ↗
Figure 2
Figure 2. Figure 2: For Model-2: Plot of q(z) with z. 5 Observational constraints and results In this section, we employ a Bayesian inference approach to assess the consistency of the proposed cos￾mological models with observational datasets. The key model parameters, H0, q0 and q1, appearing in the parametrized expressions of the Hubble parameter given in Eqs. (22) and (24), are constrained using the cosmic chronometer (CC) … view at source ↗
Figure 3
Figure 3. Figure 3: For Model-1: The best-fit H(z) curve for the proposed model is compared with the ΛCDM model. 000 0 0 0 0 00   0  00 z [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: For Model-2: The best-fit H(z) curve for the proposed model is compared with the ΛCDM model. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: For Model-1: Marginalized 1D and 2D posterior contour map with median values of H0, q0 and q1 using the Joint dataset. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: For Model-2: Marginalized 1D and 2D posterior contour map with median values of H0, q0 and q1 using the Joint dataset. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: For Model-1: Plot of energy density (ρDE) with z. −        − [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: For Model-2: Plot of energy density (ρDE) with z. −        − [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: For Model-1: Plot of EoS parameter (ωDE) with z. −        − − − [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: For Model-2: Plot of EoS parameter (ωDE) with z. 6.2 Analysis of energy conditions The point-wise energy conditions at a spacetime point, governed exclusively by the stress energy tensor, are expressed as follows [92–94]: • NEC:- The null energy condition requires that ρeff + peff ≥ 0, ensuring that the combined contribution of the effective energy density and pressure remains non-negative. • WEC:- The we… view at source ↗
Figure 13
Figure 13. Figure 13: For Model-1: Plot of the components of energy conditions with z. 6.3 Statefinder diagnostic analysis The role of geometric parameters in characterizing the cosmological evolution of a model is well established. However, to rigorously investigate alternative DE scenarios that deviate from the standard ΛCDM frame￾work, it becomes necessary to extend beyond the conventional descriptors such as the Hubble par… view at source ↗
Figure 14
Figure 14. Figure 14: For Model-2: Plot of the components of energy conditions with z. − − − −             C    [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: For Model-1: Plot of s and r plane. more sensitive and refined diagnostic of cosmic dynamics, capable of distinguishing subtle differences among competing DE models. The statefinder diagnostic, introduced through the pair {r,s} [96], serves as a pow￾erful geometrical tool for this purpose. It enables a systematic classification of DE models based on their evolutionary trajectories in the {r,s} parameter s… view at source ↗
Figure 16
Figure 16. Figure 16: For Model-2: Plot of s and r plane. 6.4 Om(z) diagnostics analysis The Om(z) diagnostic constitutes a powerful geometrical probe for distinguishing between different dark energy models [98]. For a spatially flat universe, it is given by Om(z) =  H(z) H0 2 −1 (1+z) 3 −1 . (39) The slope of the Om(z) diagnostic reflects the nature of dark energy: a positive slope indicates phantom be￾havior, while a negat… view at source ↗
Figure 17
Figure 17. Figure 17: For Model-1: Plot of Om(z) diagnostics with z. −        [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: For Model-2: Plot of Om(z) diagnostics with z. −        [PITH_FULL_IMAGE:figures/full_fig_p018_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: For Model-1: Plot of temperature with z. −        [PITH_FULL_IMAGE:figures/full_fig_p018_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: For Model-2: Plot of temperature with z. −        [PITH_FULL_IMAGE:figures/full_fig_p019_21.png] view at source ↗
read the original abstract

In this study, we probe the cosmological evolution of the universe within the framework of modified teleparallel gravity by considering a power-law form of the function $f(T)=\alpha(-T)^{n}$. To characterize the expansion dynamics, we employ logarithmic and log-periodic parametrizations of the deceleration parameter. These specific parametrizations provide a flexible and well-structured description of the cosmic expansion history across different cosmological epochs. The corresponding Hubble parameter is obtained as a function of redshift, facilitating a systematic investigation of the background dynamics. The model parameters are constrained using cosmic chronometer (CC) and joint (CC+Pantheon) datasets through a Bayesian analysis based on the $\chi^{2}$-minimization approach. The evolution of key cosmological quantities, including the deceleration parameter, energy density, pressure, equation of state parameter and energy conditions, is examined in detail. The geometrical diagnostics indicate a clear departure from the standard cosmological constant behavior, pointing toward a dynamically evolving dark energy scenario. Further, the proposed models remain thermodynamically consistent and the estimated age of the universe is found to be compatible with observational constraints, thereby reinforcing the robustness and viability of the framework.

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 / 0 minor

Summary. The paper investigates cosmological evolution in f(T) teleparallel gravity with the power-law form f(T)=α(-T)^n. It adopts logarithmic and log-periodic parametrizations of the deceleration parameter q(z) to obtain H(z) as a function of redshift, constrains the parameters via χ² minimization on cosmic chronometer and joint CC+Pantheon datasets, and examines the evolution of q(z), energy density, pressure, equation-of-state parameter, energy conditions, and geometrical diagnostics. The abstract concludes that the diagnostics show clear departure from ΛCDM (indicating dynamical dark energy), that the models are thermodynamically consistent, and that the inferred universe age is compatible with observations.

Significance. If the central results hold after addressing the derivation issue, the work would supply concrete observational bounds on power-law f(T) models using flexible expansion-history ansatzes, together with explicit checks of thermodynamic consistency and age compatibility. The use of standard CC and Pantheon data with Bayesian χ² analysis provides reproducible empirical grounding for the viability of the chosen parametrizations within the f(T) setting.

major comments (2)
  1. [Abstract] Abstract: the claim that 'geometrical diagnostics indicate a clear departure from the standard cosmological constant behavior' is load-bearing for the central conclusion of dynamically evolving dark energy. This departure is obtained from the externally imposed logarithmic and log-periodic q(z) forms rather than from solutions of the modified Friedmann equations that follow from f(T)=α(-T)^n with T=-6H². The power-law f(T) yields a specific differential equation for H(z) whose solutions are not in general logarithmic or log-periodic in z.
  2. [Methodology] Methodology (parametrization of q(z) and derivation of H(z)): the Hubble parameter is constructed directly from the chosen q(z) ansatzes and then fitted to data; the f(T) field equations are not solved to obtain H(z) or q(z). Consequently the reported evolution of energy density, pressure, and equation of state, as well as the thermodynamic and age checks, are performed on an externally prescribed expansion history rather than on a solution internal to the f(T) model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address the major points below, acknowledging where clarification and revision are needed while defending the phenomenological approach taken.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'geometrical diagnostics indicate a clear departure from the standard cosmological constant behavior' is load-bearing for the central conclusion of dynamically evolving dark energy. This departure is obtained from the externally imposed logarithmic and log-periodic q(z) forms rather than from solutions of the modified Friedmann equations that follow from f(T)=α(-T)^n with T=-6H². The power-law f(T) yields a specific differential equation for H(z) whose solutions are not in general logarithmic or log-periodic in z.

    Authors: We agree that the logarithmic and log-periodic q(z) parametrizations are imposed externally to derive H(z), and these forms are not obtained as solutions to the differential equation arising from the power-law f(T) model. The departure from ΛCDM is indeed diagnosed from the data-constrained expansion histories rather than from internal solutions of the modified Friedmann equations. Our intent was to use these flexible ansatzes as a probe within the f(T) framework to explore possible dynamical behaviors consistent with observations. We will revise the abstract to explicitly state that the diagnostics reflect the constrained parametrizations and to temper the claim of 'clear departure' by noting the phenomenological nature of the approach. revision: yes

  2. Referee: [Methodology] Methodology (parametrization of q(z) and derivation of H(z)): the Hubble parameter is constructed directly from the chosen q(z) ansatzes and then fitted to data; the f(T) field equations are not solved to obtain H(z) or q(z). Consequently the reported evolution of energy density, pressure, and equation of state, as well as the thermodynamic and age checks, are performed on an externally prescribed expansion history rather than on a solution internal to the f(T) model.

    Authors: The referee accurately notes that H(z) is obtained from the q(z) ansatzes and fitted directly to the CC and CC+Pantheon datasets via χ² minimization, without solving the f(T) field equations for H(z). The subsequent calculations of energy density, pressure, equation-of-state, energy conditions, thermodynamics, and age are performed on this externally prescribed history. This constitutes a phenomenological exploration rather than a self-consistent solution internal to the power-law f(T) model. We will revise the methodology section to clarify this distinction, add a discussion of the limitations, and explain the rationale for using flexible parametrizations to constrain viable expansion histories in the f(T) context. revision: yes

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The model introduces two phenomenological parametrizations for q(z) whose coefficients are free parameters fitted to data, plus the power-law exponent n and coefficient α in f(T). Background assumptions include the FLRW metric and the teleparallel gravity framework.

free parameters (4)
  • α
    Prefactor in the power-law f(T) = α(-T)^n
  • n
    Exponent in the power-law f(T) = α(-T)^n
  • logarithmic q(z) coefficients
    Parameters in the logarithmic deceleration ansatz fitted to data
  • log-periodic q(z) coefficients
    Parameters in the log-periodic deceleration ansatz fitted to data
axioms (2)
  • domain assumption Homogeneous and isotropic FLRW spacetime
    Standard cosmological assumption used to derive H(z) from q(z)
  • domain assumption Teleparallel equivalent of general relativity as the base theory
    Framework within which the f(T) modification is defined

pith-pipeline@v0.9.1-grok · 5745 in / 1408 out tokens · 21399 ms · 2026-06-27T06:17:55.384974+00:00 · methodology

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