Cosmological Dynamics of Accelerating Model in $f(T)$ Gravity with Special Forms of Deceleration Parameter

TL;DR

This study explores the accelerated expansion of the universe within $f(T)$ gravity, analyzing two redshift-dependent deceleration parameter models, deriving cosmological parameters, and fitting them to observational data to understand dark energy behavior.

Contribution

It introduces specific $f(T)$ gravity models with power-law forms and two novel redshift-dependent deceleration parameters, providing a detailed statistical analysis with observational data.

Findings

Models fit well with observational data.

Dark energy equation of state indicates accelerated expansion.

Current universe age consistent with observations.

Abstract

In this paper, the dynamical behavior of the accelerated expansion of the universe is discussed within the framework of $f(T)$ gravity, considering power law functional form of $ f(T)=\alpha (-T)^{n}$. Two distinct redshift-dependent parameterization of the deceleration parameter such as $q(z)=q_{0}+ q_{1}\left(\frac{ \ln(N+z)}{z+1}-\ln N \right)$ and $ q(z)=\frac{1}{2}+ \frac{q_{1}z+ q_{2}}{(1+z)^2} $ are considered. We have derived the Hubble parameter in terms of redshift and discussed its effect on other cosmological parameters. Using Bayesian statistical analysis and $\chi^2$-minimization, the median values of the model parameters for both the cosmic chronometer(CC) and the joint(CC + Pantheon) dataset have been determined. Further, energy density, pressure, the equation of state for Dark Energy, Energy condition and statefinder diagnostics are analyzed. The current age of the universe is also computed for these models.