Probing Quintessence with Time Variation of Couplings
  Many models of quintessence predict a time variation of the fundamental constants as well as a composition-dependent gravity like long-range force mediated by the cosmon. We present bounds for the cosmon coupling to matter and radiation within a grand unified framework. The unification scale, the unified gauge coupling and the Fermi scale are allowed to vary independently. We find that the variation of the weak scale compared to the nucleon mass is severely restricted. The violation of the equivalence principle turns out to be substantially larger than in models where only the electromagnetic fine structure constant varies with time. We also show that in contrast to gravity the local cosmon field in a condensed object does not decouple from the cosmological evolution. In consequence, the cosmon interaction constitutes a possible quantitative link between cosmological observations and several areas of high precision experiments concerning the local time or space variation of couplings and tests of the equivalence principle. 
C.Wetterich