Cosmological Study of Autonomous Dynamical Systems
Cosmological approaches of autonomous dynamical system 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, consist to extract dynamical systems whose time-dependence is contained in a single parameter m depending on the Hubble rate of Universe and its second derivative. In our attempt to investigate the autonomous aspect of the dynamical systems reconstructed in both vacuum and non-vacuum f(T ) gravities, two values of the parameter m have been considered for our present analysis. In the so-called quasi-de Sitter inflationary era (m ≃ 0), the corresponding autonomous dynamical systems provide stable de Sitter attractors and unstable de Sitter fixed points. Especially in the vacuum f(T ) gravity, the approximate form of the f(T ) gravity near the stable and the unstable de Sitter fixed points has been performed. The matter dominated era case (m = −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 matter dominated case in the non-vacuum f(T ) gravity is when the dark energy dominated era is reached, at the same time, the radiation perfect fluid dominated succumbs.
It has been supported that in addition to the inflationary stage  in the early Universe, the current accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) ,Type Ia Supernovae , large scale structure , baryon acoustic oscillations (BAO)  as well as weak lensing  and Sloan Digital Sky Survey (SDSS) . In an attempt to explain this phenomenon there are two possible paths; the first option proposes corrections to General Relativity as the cosmological constant, the second assumption assuming that there is a dominant component of the universe, called dark energy.
de Sitter, inflation, Autonomous, fixed point, dark energy, Tele-Parallel
Ganiou, M.G., Logbo, P.H., Houndjo, M.J.S., Tossa, J. (2018). Cosmological Study of Autonomous Dynamical Systems in Modified Tele-Parallel Gravity. Pg 1-25