Local Experiments See Cosmologically Varying Constants
  We describe a rigorous construction, using matched asymptotic expansions, which establishes under very general conditions that local terrestrial and solar-system experiments will measure the effects of varying `constants' of Nature occurring on cosmological scales to computable precision. In particular, `constants' driven by scalar fields will still be found to evolve in time when observed within virialised structures like clusters, galaxies, and planetary systems. This provides a justification for combining cosmological and terrestrial constraints on the possible time variation of many assumed `constants' of Nature, including the fine structure constant and Newton's gravitation constant. 
Douglas J. Shaw and John D. Barrow