Constraining scalar-tensor quintessence by cosmic clocks

Scalar-tensor quintessence models can be constrained by identifying suitable cosmic clocks which allow to select confidence regions for cosmological parameters. In particular, we constrain the characterizing parameters of non-minimally coupled scalar-tensor cosmological models which admit exact solutions of the Einstein field equations. Lookback time to galaxy clusters at low intermediate, and high redshifts is considered. The high redshift time-scale problem is also discussed in order to select other cosmic clocks such as quasars.