A new parametric study of $f(T)$ teleparallel gravity with generalized Chaplygin gas: Confronting observational data

Abstract

In this paper, we investigate the cosmological dynamics of a modified gravity framework based on the function $f(T)=β(-T)^{1/2}+γ(-T)$, where $T$ denotes the torsion scalar. The matter sector is modeled using the Generalized Chaplygin Gas (GCG) with the equation of state $p=-\frac{\mathcal{A}}{ρ^η}$, allowing the model to describe the evolution from an early-time matter-like phase to a late-time accelerated universe. By deriving an analytical expression for the Hubble parameter $H(z)$, we perform parameter estimation using Bayesian statistical techniques based on the $χ^{2}$-minimization method with the Cosmic Chronometer (CC) and joint (CC+Pantheon) observational datasets. The deceleration parameter exhibits a transition from deceleration to acceleration, while the present-day value indicates the current accelerated expansion. The model yields a present-day EoS parameter consistent with dark-energy-like behavior, while the energy conditions indicate that the NEC and DEC are satisfied and the SEC is violated at late times. The $ω-ω'$ plane shows a freezing quintessence behavior, approaching the $Λ$CDM-like point $(ω,ω')=(-1,0)$, while the cosmographic analysis offers additional insight into the evolution of the cosmic expansion. The estimated age of the universe is also consistent with current observational bounds. These results demonstrate that the GCG scenario within $f(T)$ teleparallel gravity provides a viable and observationally consistent framework for explaining the late-time accelerated expansion of the universe.