Cosmological Perturbations in Restricted f(R)-Gravity

We investigate the metric perturbations of the restricted f(R) theory of gravity in the cosmological context and explore the phenomenological implications of this model. We show that it is possible to construct a restricted model of gravity, in which the background equations are the same as the equations of motion which are derived from the Einstein-Hilbert action with the cosmological constant term. We argue that the deviation from the Einstein-Hilbert model emerges in the perturbed equations, for which we have a non-vanishing anisotropic stress. Further, with the help of the results of Planck data for the modified gravity we obtain constraints on the parameters of the model.