F(T, R) theory of gravity

We mainly focus on the idea that the dynamics of the whole universe may be understood by making use of torsion T and curvature R at the same time. The f(T,R)-gravity can be considered as a fundamental gravitational theory describing the evolution of the universe. The model can produce the unification of the general relativity (GR), teleparallel gravity (TPG), f(R)-gravity and f(T)-gravity theories. For this purpose, the corresponding Lagrangian density is written in terms of an arbitrary function of the torsion and curvature scalars. Furthermore, we use the absence/existence puzzle of relativistic neutron stars and thermodynamical laws as constraining tools for the new proposal.