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 $x={\rho }_e/(3m_{pl}^2{H}^2)$ and $T=g(x)$, the system is an autonomous one. Furthermore,the ${\omega }_e-{\omega }_e^{\prime }$ 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 ${\omega }_{ep}-{\omega }_{ep}^{\prime }$ plane.

13 pages, 2 figures

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