Variation of the constants in the late and early universe

Abstract

Recent key observational results on the variation of fine structure constant, the proton to electron mass ratio and the gravitational constant are reviewed. The necessity to substantiate the dark sector of cosmology and to test gravity on astrophysical scales is also emphasized.Comment: 19 pages, 6 figures, Invited talk at the conference "The Quest for Cosmological Scalar Fields", Porto, 8-10 July 200