Cosmological Parameters in $f(T)$ Gravity: Theoretical and Observational Analysis

TL;DR

This paper investigates a specific $f(T)$ gravity model using dynamical systems and observational data, demonstrating its ability to replicate the Universe's expansion history and constrain model parameters.

Contribution

It introduces a new functional form of $f(T)$ gravity, analyzes its stability and cosmological behavior, and constrains parameters with recent observational datasets.

Findings

The model's stability conditions are consistent with best-fit parameters.

Phase-space analysis reveals transitions between cosmic epochs.

Observational data constrain parameters within the stability range.

Abstract

The $f(T)$ gravity is one of the extensions of teleparallel equivalent of general relativity, in which more general functions of the torsion scalar $T$ can be described. With the proposed functional form of $f(T) = \alpha T - \beta u^{-n} + \gamma u^m$, where $u = (-T/6)$, we have analyzed the cosmological parameters using dynamical system analysis and cosmological datasets. The dynamical behavior of this model is analyzed with phase-space analysis by transforming the cosmological equations into an autonomous system. Critical points are identified, and their stability conditions examined, enabling the classifications of the early and late-time evolutionary phases of the Universe. The stability conditions are further demonstrated by phase-portrait diagrams that highlight transitions between radiation, matter, and dark-energy-dominated epochs. Then we used the Markov Chain Monte Carlo statistical technique to constrain the model parameters with the recent observational dataset, such as DESI DR2 BAO, and its combination with the Hubble and Pantheon+SH0ES data. The best-fit values for the model parameters were obtained by data analysis, $m \equiv 0.91^{+0.07}_{-0.09}$ and $n \equiv 0.69^{+0.09}_{-0.08}$, and are well within the stability range obtained ($m<1\land n>-1$) through dynamical system analysis. The combined theoretical and observational analysis shows that the proposed $f(T)$ gravity model successfully reproduces the observed cosmic expansion history of the Universe.