Cosmological study of autonomous dynamical systems in modified Tele-Parallel gravity

Abstract.

Cosmological approaches of an autonomous dynamical system studied in the framework of f(T) gravity are investigated in this paper. Our methods applied to flat Friedmann-Robertson-Walker equations in f(T) gravity, consisting in extracting dynamical systems whose time-dependence is contained in a single parameter m depending on the Hubble rate of the Universe and its second derivative order. In our attempt to investigate the autonomous aspect of the dynamical systems reconstructed in both vacuum and non-vacuum f (T) gravities, two constant values of the parameter m have been at the heart of our present analysis. In the so-called quasi-de Sitter inflationary era ($m\simeq 0$), the corresponding autonomous dynamical systems provide stable de Sitter attractors and unstable de Sitter fixed points. Especially in vacuum f(T) gravity, the approximate form of the f(T) gravities near the stable and the unstable de Sitter fixed points has been performed. The matter dominated era case $(m=-\frac{9}{2})$ leads to unstable fixed points confirming matter dominated era or not, and stable attractor fixed point describing dark energy dominated era. Another subtlety around the stable fixed point obtained at the matter dominated case in the non-vacuum f(T) gravity is that when the dark energy dominated era is reached, at the same time, the radiation perfect fluid dominated succumbs.