Brane-world cosmology and varying G

The rst ideas of a varying Newton's coupling G come from 1937, when P. A. M. Dirac introduced his famous Large Numbers Hypothesis [1, 2]. In the 60s, in an attempt to reconciliate Mach Principle with General Relativity (GR), Brans and Dicke developed their well known scalar-tensor theory of gravity [3]. Following Jordan's ideas, Brans and Dicke generalized GR including a varying G, whose dynamics was governed by a scalar eld. See [4] for a detailed review on varying fundamental constants. In addition to the e ects of introducing a dynamical coupling constant, we know that gravitational interaction is also sensitive to the existence of extra dimensions, which could manifest themselves at short distances. In this paper, we will be concerned with models that incorporate both a varying G and a higher dimensional set up. Although the idea of extra dimensions is not new either [5, 6], the advent of modern (string) theories has brought to the fore the higher dimensional