Brane-world cosmology and varying $G$

We consider a brane-world cosmological model coupled to a bulk scalar field. Since the brane tension turns out to be proportional to Newton coupling $G$, in such a model a time variation of $G$ naturally occurs. By resorting to available bounds on the variation of $G$, the parameters of the model are constrained. The constraints coming from nucleosynthesis and CMB result to be the severest ones.