Cosmological Perturbations In F(T) Gravity

The cause for the late-time accelerated expansion of the universe remains one ofthe most compelling problems in modern physics during the last decade. Cosmologistshave contrived many schemes to account for this phenomena, the most prevailing ofwhich goes to the dark energy scenario. However, modifying gravity also serves to bean competent alternative to this ends. For instance, an extra scalar field can be intro-duced to non-minimally couple with gravity, or the Eintein-Hilbert Lagrangian can beextended to a function of Ricci scalar. These theories are based on the convention thatthe gravity be described as the curvature of the background spacetime. However, dat-ing back to Einstein, another explanation of gravity is taking advantage of the torsion,rather than curvature of the background manifold. In this case, torsion would play therole as curvature in GR. Accordingly, a torsion scalar T can be defined to constitute thesimplest Lagrangian in this formulation. In analogy to the introduction of f(R) gravity,one can also generalize the Lagrangian to be a function of the torsion scalar T, that is,the f(T) theory.In this theory, there is no local Lorentz symmetry. Compared with GR, some extradegrees of freedom would arise, which do not show up in the expression of the metric,andthushavetobedefinedintetrad. Unfortunately,thispointhasbeentakenforgrantedin previous literatures. Variating the action with respect to the tetrad gives rise to theequations of motion and further the background and first-order equations. In this paper,we are mainly concerned with the evolution of large scale structure of the universe atlate time universe, when the pressure and its perturbation vanish simultaneously. Wederive the governing equation for the fractional density perturbation and find that ittakes a similar form as that in GR, except for a redefined gravitational constant. Wesolve this equation numerically and contrast the result with that in GR.