f(T) cosmology: from Pseudo-Bang to Pseudo-Rip

We investigate the complete universe evolution in the framework of f(T) cosmology. We first study the requirements at the kinematic level and we introduce a simple scale factor with the necessary features. Performing a detailed analysis of the phase portrait we show that the universe begins in the infinite past from a phase where the scale factor goes to zero but the Hubble parameter goes to a constant, and its derivative to zero. Since these features resemble those of the Pseudo-Rip fate but in a revered way, we call this initial phase as Pseudo-Bang. Then the universe evolves in a first inflationary phase, a cosmological turnaround and a bounce, after which we have a second inflationary regime with a successful exit. Subsequently we obtain the standard thermal history and the sequence of radiation, matter and late-time acceleration epochs, showing that the universe will result in an everlasting Pseudo-Rip phase. Finally, taking advantage of the fact that the field equations of f(T) gravity are of second order, and therefore the corresponding autonomous dynamical system is one dimensional, we incorporate the aforementioned kinematic features and we reconstruct the specific f(T) form that can dynamically generate the Pseudo-Bang cosmological scenario. Lastly, we examine the evolution of the primordial fluctuations showing that they are initially sub-horizon, and we show that the total fluid does not exhibit any singular behaviour at the phantom crossing points, while the torsional fluid experiences them as Type II singular phases. (paper)