f(T) theories from holographic dark energy models within Bianchi type I universe

Recently, the teleparallel Lagrangian density described by the torsion scalar T has been extended to a function of T. The f(T) modified teleparallel gravity has been proposed as the natural gravitational alternative for dark energy to explain the late time acceleration of the universe. We consider spatially homogenous and anisotropic Bianchi type I universe in the context of f(T) gravity. The purpose of this work is to develop a reconstruction of the f(T) gravity model according to the holographic dark energy model. We have considered an action, of the form T + g(T) + L m, describing Einstein’s gravity plus a function of the torsion scalar. In the framework of the said modified gravity theory, we have considered the equation of state of the holographic dark energy density. Subsequently, we have developed a reconstruction scheme for modified gravity with f(T) action. Finally, we have also studied the de Sitter and power-law solutions when the universe enters a phantom phase and shown that such solutions may exist for some f(T) solutions with the holographic and new agegraphic dark energy scenario.