Notes on $f(T)$ Theories

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 $x=ρ_{e}/(3m_{pl}^{2}H^{2})$ and $T=g(x)$, the system is an autonomous one. Furthermore,the $ω_{e}-ω'_{e}$ phase analysis is given out. We perform the dynamical analysis for the models $f(T)=βT\ln(T/T_{0})$ and $f(T)=αm_{pl}^{2}(-T/m_{pl}^{2})^{n}$ 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 $ω_{ep}-ω'_{ep}$ plane.

13 pages, 2 figures