Title: "Holography, modified gravity and extra-dimensions"

Abstract: On this talk we will describe the brane-world scenario as a mean to account for the late-time acceleration of the universe. We will address two issues: on the one hand, we propose a generalised induced gravity brane-world model where the brane action contains an arbitrary f(R) term, R being the scalar curvature of the brane. We show that the effect of the f(R) term on the dynamics of a homogeneous and isotropic brane is twofold: (i) an evolving induced gravity parameter and (ii) a shift on the energy density of the brane. This new shift term, which is absent on the Dvali, Gabadadze and Porrati (DGP) model, plays a crucial role to self-accelerate the generalised normal DGP branch of our model. We analyse as well the stability of de Sitter self-accelerating solutions under homogeneous perturbations and compare our results with the standard 4-dimensional one. We will as well apply a cosmographic approach to constrain the present model. On the other hand, we present an holographic model of the DGP scenario with a Gauss-Bonnet term in the bulk. We concentrate on the solution that generalises the normal DGP branch. It is well known that this branch cannot describe the late-time acceleration of the universe even with the inclusion of a Gauss-Bonnet term. Here, we show that this branch in the presence of a Gauss-Bonnet curvature effect and an holographic dark energy with the Hubble scale as the infra-red cutoff can describe the late-time acceleration of the universe. It is worthwhile to stress that such an energy density component cannot do the same job on the normal DGP branch (without Gauss-Bonnet modifications) nor in a standard 4-dimensional relativistic model. The acceleration on the brane is also presented as being induced through an effective dark energy which corresponds to a balance between the holographic one and geometrical effects encoded through the Hubble parameter.