Notes on $f(T)$ Theories

TL;DR

This paper analyzes the phase-space dynamics of $f(T)$ teleparallel gravity models, demonstrating conditions for autonomous systems and the universe's evolution towards de-Sitter phases, with specific models examined.

Contribution

It provides a phase-space analysis framework for $f(T)$ theories and explores their cosmological evolution, including specific model behaviors and stability.

Findings

Universe tends to a de-Sitter phase in studied models

Phase-space analysis reveals conditions for autonomous system behavior

Power-law models exhibit characteristic evolution in $ ext{w}_e- ext{w}_e'$ plane

Abstract

The cosmological models based on teleparallel gravity with nonzero torsion are considered. To investigate the evolution of this theory, we consider the phase-space analysis of the $f(T)$ theory. It shows when the tension scalar can be written as an inverse function of $x$ where $x=\rho_{e}/(3m_{pl}^{2}H^{2})$ and $T=g(x)$, the system is an autonomous one. Furthermore,the $\omega_{e}-\omega'_{e}$ phase analysis is given out. We perform the dynamical analysis for the models $f(T)=\beta T\ln(T/T_{0})$ and $f(T)=\alpha m_{pl}^{2}(-T/m_{pl}^{2})^{n}$ particularly. We find that the universe will settle into de-Sitter phase for both models. And we have examined the evolution behavior of the power law form in the $\omega_{ep}-\omega'_{ep}$ plane.