Phase space analysis of the evolution of the early universe in Einstein-Cartan theory

In this paper, we perform the phase space analysis to investigate the evolution of the early universe in Einstein-Cartan theory. By studying the stability of critical points in dynamical system, it is found that there exist two stable critical points which represent an expanding solution and an Einstein static solution respectively. After analyzing the phase diagram of the dynamical system, we find that there may exist a bouncing universe, an oscillating universe or an Einstein static universe in the early time of universe. In addition, by assuming that the early universe filled by the radiation with ω= 1/3 , the initial states of the early universe are Einstein static universe or oscillating universe. When the equation of state ω decreases with time, the universe can exit from the initial state and evolve into an expanding phase.