Bouncing Scenario in the $f(T)$ Modified Gravity Model with Dynamical System Analysis

TL;DR

This paper investigates the bouncing cosmological scenario within the $f(T)$ modified gravity framework using dynamical system analysis to explore stability and universe evolution.

Contribution

It introduces a dynamical system approach to analyze bouncing solutions in $f(T)$ gravity, highlighting stability and cosmological implications.

Findings

Identification of stable fixed points in the phase space.

Demonstration of conditions for a bouncing universe.

Analysis of the stability of cosmological solutions.

Abstract

In $f(T)$ gravity, the theory modifies the gravitational action by introducing a function of the torsion scalar $T$. This approach allows for a different treatment of gravity than general relativity, particularly in cosmological contexts. Dynamical system analysis is a powerful tool for exploring the stability and behavior of cosmological solutions within this framework. The dynamical system analysis involves examining the phase space of the cosmological equations derived from the $f(T)$ model. This analysis helps identify fixed points, stability, and the evolution of the universe's scale factor. Therefore, in the following, we first review the main equations of the $f(T)$ gravity model. Then we study the dynamic analysis of the gravity model and obtain stability points. Finally, we consider the bouncing scenario in this model.