  Scalar field dynamics may give rise to a nonzero cosmological variation of
fundamental constants. Within different scenarios based on the unification of
gauge couplings, the various claimed observations and bounds may be combined in
order to trace or restrict the time history of the couplings and masses. If the
scalar field is responsible for a dynamical dark energy or quintessence,
cosmological information becomes available for its time evolution. Combining
this information with the time variation of couplings, one can determine the
interaction strength between the scalar and atoms, which may be observed by
tests of the Weak Equivalence Principle. We compute bounds on the present rate
of coupling variation from experiments testing the differential accelerations
for bodies with equal mass and different composition and compare the
sensitivity of various methods. In particular, we discuss two specific models
of scalar evolution: crossover quintessence and growing neutrino models.
