Title: "Brane-world induced gravity: early and late-time behaviour"

In this talk, we will review the induced gravity brane-world scenario. On the one hand, we will show how the induced gravity affects the early-time evolution of the brane through corrections to the Randall-Sundrum type cosmology. In particular, we will analyse the effect of these corrections in the amplitude of the primordial gravitational waves on large scale as well as the amplitude of the scalar perturbations on the brane (with respect to the Randall-Sundrum case and the standard 4-dimensional case). The analysis is performed on the extreme slow-roll limit for an inflaton confined to the brane. On the other hand, the induced gravity, in the context of the Dvali-Gabadadze-Porrati model, can describe the late-time speed up of the universe or induce a mimicry of a phantom-like behaviour on the brane. The mimicry is achieved without invoking any matter that violates the null energy condition on the brane and is based in defining an effective energy density which corresponds to a balance between dark energy and geometrical effects. Depending on the dynamical character of the dark energy, this effective energy density can either mimic a phantom-like behaviour or even a crossing of the cosmological constant line.