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The framework for considering the astronomical and cosmological observations in the context of scalar-tensor quintessence in which the quintessence field also accounts for a time dependence of the gravitational constant is developed. The constraints arising from nucleosynthesis, the variation of the constant, and the post-Newtonian measurements are taken into account. A simple model of supernovae is presented in order to extract the dependence of their light curves with the gravitational constant; this implies a correction when fitting the luminosity distance. The properties of perturbations as well as CMB anisotropies are also investigated.
Riazuelo et al. (Wed,) studied this question.