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

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 $f(T) = α$(-T)^{n},</sup>inconjunctionwiththeGong−ZhangparametrizationofthedarkenergyEoS.Wederivetheexpansionrateintermsoftheredshiftfortheconsideredmodel,providingdeeperinsightsintotheunderlyingcosmicdynamics.Themodelisfurtherutilizedtoexploretheexpansionhistoryoftheuniverseandtheevolutionofseveralcosmologicalparameters.ByusingtheBayesianmethodsbasedonthe,</sup> 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 χ^{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.

• The paper develops a novel f(T) teleparallel model combining power-law dynamics with Gong-Zhang dark energy parametrization to explain transient cosmic acceleration.
• It derives explicit analytical solutions for H(z) and q(z), and constrains model parameters using cosmic chronometer and Pantheon supernova data.
• The model predicts a shift from present acceleration to future deceleration while satisfying energy conditions and thermodynamic laws.

Transient Phenomenology in $f(T)$ Teleparallel Gravity with Gong-Zhang Parametrization

Theoretical Framework

This study develops the cosmic expansion dynamics within the power-law $f(T) = \alpha (-T)^n$ teleparallel gravity framework, employing the Gong-Zhang parametrization for the dark energy (DE) equation of state (EoS). $f(T)$ gravity modifies the teleparallel equivalent of general relativity (TEGR) by replacing the torsion scalar $T$ with an arbitrary function, leading to second-order field equations distinct from the metric-based $f(R)$ paradigm. The model assumes a spatially flat FLRW metric and directly parametrizes the DE EoS as

$$\omega_{\rm DE}(z) = \frac{\omega_0}{1+z} \exp\left(\frac{z}{1+z}\right),$$

where $\omega_0$ is the present EoS value. This choice ensures that DE smoothly interpolates between an effectively pressureless fluid ($\omega_{\rm DE} \to 0$) at high redshift and dynamically evolves at low redshift, with a return to $\omega_{\rm DE} \to 0$ in the asymptotic future.

The paper derives explicit analytical solutions for the Hubble parameter $H(z)$, the deceleration parameter $f(T) = \alpha (-T)^n$0, energy density, and pressure in terms of cosmological redshift, based on the modified field equations. These expressions encapsulate the influence of the $f(T) = \alpha (-T)^n$1 functional and the Gong-Zhang EoS across cosmic history.

Observational Confrontation and Statistical Constraints

Model parameters $f(T) = \alpha (-T)^n$2 are tightly constrained via Bayesian inference using both the state-of-the-art cosmic chronometer (CC) dataset and the joint CC+Pantheon supernova compilation. The MCMC likelihood framework minimizes the total chi-square over Hubble rate and luminosity distance measurements. Median constraints for the joint dataset converge to $f(T) = \alpha (-T)^n$3, $f(T) = \alpha (-T)^n$4, and $f(T) = \alpha (-T)^n$5, with posterior uncertainties consistent with recent large-scale structure and cosmic microwave background (CMB) results.

Key outputs, such as the present deceleration parameter $f(T) = \alpha (-T)^n$6 and the transition redshift $f(T) = \alpha (-T)^n$7 to acceleration, are directly inferred. Notably, $f(T) = \alpha (-T)^n$8 and $f(T) = \alpha (-T)^n$9 from the joint constraints, matching observationally inferred values. The model robustly aligns with the empirical age of the universe ($f(T)$0 Gyr) and provides accurate fits for $f(T)$1 evolution across $f(T)$2.

Dynamical Evolution and Physical Characterization

Deceleration and Cosmic Evolution

The analysis reveals a key result: the current accelerated expansion is a transient phenomenon, with a predicted future return to deceleration. This is in direct contrast to $f(T)$3CDM, where acceleration persists indefinitely. The deceleration parameter $f(T)$4 transitions from $f(T)$5 (deceleration) to $f(T)$6 (acceleration) near $f(T)$7, remaining negative in the current epoch but approaching zero and eventually positive values in the future. This behavior stems from the evolution of the EoS, which dynamically interpolates between matter-like and quintessence-like regimes.

Energy Density, Pressure, and EoS Evolution

Dark energy density $f(T)$8 is consistently positive, and pressure $f(T)$9 is negative at $T$0, ensuring physical viability and supporting late-time acceleration. The EoS parameter at present sits in the quintessence regime ($T$1), with $T$2 as $T$3, signaling the eventual dominance of matter-like behavior and deceleration.

Energy Conditions

The model satisfies the Null, Weak, and Dominant Energy Conditions (NEC, WEC, DEC) throughout cosmic history. The Strong Energy Condition (SEC) is violated at $T$4, a criterion directly linked to acceleration, but is restored in the future as the universe transitions back to deceleration. This feature provides a dynamical mechanism for cosmic slowing without the need for fine-tuning.

Geometrical and Dynamical Diagnostics

The study employs multiple model discrimination tools:

• Statefinder: The evolutionary tracks in the $T$5 plane begin in the Chaplygin gas regime, cross $T$6CDM, and occupy the quintessence region at present, confirming departure from a pure cosmological constant scenario.
• Om$T$7 diagnostic: Yields a negative slope at $T$8, independently corroborating the quintessence-like dynamics and deviation from $T$9CDM.
• $f(R)$0-$f(R)$1 plane: The model remains in the freezing region ($f(R)$2, $f(R)$3), with EoS approaching zero at late times. The closed-loop trajectory signifies non-trivial DE dynamics and future deceleration.

Thermodynamic Consistency

The model satisfies the generalized second law of thermodynamics (GSLT) for all $f(R)$4, with the total entropy monotonically increasing. This affirms the extended $f(R)$5 scenario is not only phenomenologically viable but consistent with the underlying causal structure and thermodynamic expectations for a dynamic horizon.

Implications and Future Directions

This analysis establishes that the $f(R)$6 power-law model, combined with Gong-Zhang EoS parametrization, encapsulates a dynamically rich alternative to $f(R)$7CDM. The transient acceleration and future deceleration feature, arising without explicit dark sector coupling or fine-tuning, offers a clear, testable prediction that can be distinguished in high-precision dataset analyses. The model's preservation of positive energy density, the restoration of the SEC in the future, and its thermodynamic consistency reinforce its theoretical soundness.

For future pursuits, the analytic tractability of the formalism allows for systematic extensions: inclusion of perturbation-level cosmological tests, consideration of non-minimal couplings, or incorporation of additional observational probes such as baryon acoustic oscillations and gravitational lensing. The predicted deceleration epoch provides a discriminant target for next-generation cosmological surveys.

Conclusion

The paper rigorously constructs and statistically validates a cosmological model in $f(R)$8 teleparallel gravity featuring the Gong-Zhang EoS. The scenario accurately describes current expansion history and matches major cosmological constraints, while predicting that acceleration is an epochal, not eternal, phenomenon. This provides a theoretically robust and observationally falsifiable alternative to the $f(R)$9CDM paradigm, highlighting the necessity of dynamical dark energy investigation in the landscape of modified gravity.