The variation of the gravitational constant inferred from the Hubble   diagram of Type Ia supernovae
  We consider a cosmological model with a variable gravitational constant, G, based on a scalar-tensor theory. Using the recent observational data for the Hubble diagram of type Ia supernovae (SNeIa) we find a phenomenological expression describing the variation of G. The corresponding variation of the fine structure constant \alpha within multidimensional theories is also computed and is shown not to support known constraints on \Delta \alpha / \alpha. 
E. Garcia-Berro, Yu.A. Kubyshin, P. Loren-Aguilar, and J. Isern