Studies in f (T)Theories

Abstract

The Standard FRW(Big-Bang) Cosmology has succeeded to trace the cosmic thermal evolution in an elegant way by comparing the particles interactions rate with the expansion rate of the Universe. At very hot stages, the rate of particle interactions is much larger than the expansion rate of the Universe and local thermal equilibrium could be achieved. At later stages, when the Universe cools down, the interaction rate decreases faster than the expansion allowing the particles to decouple from the thermal path at the equality of the rates. On the other hand, the Standard big-bang Cosmology suffers many problems, e.g., Initial Singularity, flatness, particle horizons, etc. Solving these problems requires a superfast accelerated expansion phase at some early time, i.e., cosmic inflation [6, 57, 93, 116, 123], which is usually represented by an exponential expansion at 10􀀀35 s after the big-bang. As a result, the Universe becomes isotropic, homogeneous and approximately flat. Standard inflation models assume the existence of a self-coupled scalar field (inflaton) minimally coupled to gravity, whose potential governs the evolution of the Universe during inflation. During this stage, the initial quantum fluctuations cross the horizons and transform into classical fluctuations producing a nearly scale-invariant scalar perturbations spectrum. Although inflation solves the above mentioned problems, one of the fundamental problems still exists, that is the initial singularity which arises when tracing the Universe back in time as divergences of the cosmic temperature and density. Since the initial singularity is before inflation raids, the problem can not be solved within inflationary Cosmology. Another serious problem is the trans-Planckian problem which also appears in inflationary cosmology where the cosmological scales that we observe at present time correspond to length scales smaller than the Planck length at the onset of inflation [22, 98].