Phenomenological constraints on a scale-dependent gravitational coupling

We investigate the astrophysical and cosmological implications of the recently proposed idea of a running gravitational coupling on macroscopic scales. We find that when applied to the rotation curves of galaxies, their flatness requires still the presence of dark matter. Bounds on the variation of the gravitational coupling from primordial nucleosynthesis, change of the period of binary pulsars, gravitational lensing and the cosmic virial theorem are analysed.