Can f(T) gravity theories mimic ΛCDM cosmic history

Abstract

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. In order to reconstruct the function f(T) by demanding a background ΛCDM cosmology we assume that, (i) the background cosmic history provided by the flat ΛCDM (the radiation ere with ωeff = (1/3), matter and de Sitter eras with ωeff = 0 and ωeff = −1, respectively) (ii) the radiation dominate in the radiation era with Ω0r = 1 and the matter dominate during the matter phases when Ω0m = 1. We find the cosmological dynamical system which can obey the ΛCDM cosmic history. In each era, we find a critical lines that, the radiation dominated and the matter dominated are one points of them in the radiation and matter phases, respectively. Also, we drive the cosmologically viability condition for these models. We investigate the stability condition with respect to the homogeneous scalar perturbations in each era and we obtain the stability conditions for the fixed points in each eras. Finally, we reconstruct the function f(T) which mimics cosmic expansion history.