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Scalar field dynamics may give rise to a nonzero cosmological variation offundamental constants. Within different scenarios based on the unification ofgauge couplings, the various claimed observations and bounds may be combined inorder to trace or restrict the time history of the couplings and masses. If thescalar field is responsible for a dynamical dark energy or quintessence,cosmological information becomes available for its time evolution. Combiningthis information with the time variation of couplings, one can determine theinteraction strength between the scalar and atoms, which may be observed bytests of the Weak Equivalence Principle. We compute bounds on the present rateof coupling variation from experiments testing the differential accelerationsfor bodies with equal mass and different composition and compare thesensitivity of various methods. In particular, we discuss two specific modelsof scalar evolution: crossover quintessence and growing neutrino models.

Time variation of fundamental couplings and dynamical dark energy