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.