Cosmological study of finite-time singularities under dynamical systems survey in covariant modified teleparallel gravity

Abstract

In the present study, we deal with the cosmological evolution under autonomous and non-autonomous dynamical systems in the framework of covariant f(T) gravity where T is the scalar torsion. This work first investigates how the dynamical system survey can provide significant explanation near the cosmological finite-time singularities and then extracts the corresponding f(T) models. By studying the de Sitter evolution of the autonomous dynamical system generated from the Friedman equation in a vacuum, we obtain one equilibrium fixed point that describes a universe in accelerated expansion. A similar description is made with finite-time singularity where dynamical systems become necessarily non-autonomous. Near the Big-Rip singularity, an analytical resolution approach leads to finite values for the dynamic variables, which not only reveals an accelerated expanding universe but also makes it possible to reconstruct the corresponding f(T) models. In the case of the three other types of singularity, only type IV leads to an analytical solvable problem, and two of the asymptotic fixed-point coordinates diverge. Furthermore, using a classical approach based on the Hubble parameter of finite-time singularities combined with both Friedman and conservation equations, we provide in the first hand implicit f(T) models for all types of singularity and in the second hand explicit f(T) models whose stability is undertaken near each type of singularity in three different evolutions: de Sitter evolution, quintessence-like evolution, and the phantom-like evolution. The relative stability of the reconstructed models not only shows that they cannot describe all four types of singularity simultaneously but also proves that the cosmological evolution is not the same for the four types of singularity. These results confirm those obtained using the dynamical approach. The finite-time singularity avoidance is discussed at the end of the present investigation.