A new approach to modified gravity models

We investigate f (R)-gravity models performing the ADM-slicing of standard General Relativity. We extract the static, spherically-symmetric vacuum solutions in the general case, which correspond to either Schwarzschild de-Sitter or Schwarzschild anti-de-Sitter ones. Additionally, we study the cosmological evolution of a homogeneous and isotropic universe, which is governed by an algebraic and not a differential equation. We show that the universe admits solutions corresponding to acceleration at late cosmological epochs, without the need of fine-tuning the model-parameters or the initial conditions.