Effective gravitational equations on brane world with induced gravity described by f(R) term

In this article we study a generalization of Dvali-Gabadadze-Porrati scenarios, where the effective theory of gravity induced on the brane is given by a f(R) term. We obtain the effective gravitational equations and the effective FLRW cosmological equation on the brane of this model. We show that this generalization has also two regime, a 5D regime a low energies that has a self-accelerated branch of interest for cosmology and a 4D regime at high energies that it is described a modified gravitational theory.