کیومرث کرمی

In the framework of modified gravity (MG), recently a new MG theory, namely the so-called f(T) theory, attracted much attention in the community, where T is the torsion scalar. It has been demonstrated that the f(T) theory can not only explain the present cosmic acceleration with no need of dark energy, but also provide an alternative to inflation without an inflaton. f(T) theory is based on the old idea of teleparallel gravity (TG), in which the Weitzenbock connection rather than the Levi-Civita connection is used. As a result, the space-time has only torsion and thus is curvature-free. In fact, this approach was taken by Einstein in an attempt of unifying gravity and electromagnetism. Although TG is closely related to standard general relativity (GR), differing only in terms involving total derivatives in the action, i.e. boundary terms, there are some fundamental conceptual differences between them. According to GR, gravity curves the space-time and shapes the geometry. In TG however torsion does not shape the geometry but instead acts as a force. This means that there are no geodesic equations in TG but there are force equations much like the Lorentz force in electrodynamics. f(T) theory is obtained by extending the action of TG in analogy to the f(R) theory. An important advantage of f(T) theory is that its field equations are second order as opposed to the fourth order equations of f(R) gravity. This feature has led to a rapidly increasing interest in the literature. Here, we review f(T)-gravity and discuss some theoretical and observational aspects of this kind of MG in cosmology.