Quintessence, super-quintessence and observable quantities in   Brans-Dicke and non-minimally coupled theories
  The different definitions for the equation of state of a non-minimally coupled scalar field that have been introduced in the literature are analyzed. Particular emphasis is made upon those features that could yield to an observable way of distinguishing non-minimally coupled theories from General Relativity, with the same or with alternate potentials. It is found that some earlier claims on that super-quintessence, a stage of super-accelerated expansion of the universe, is possible within realistic non-minimally coupled theories are the result of an arguable definition of the equation of state. In particular, it is shown that these previous results do not import any observable consequence, i.e. that the theories are observationally identical to General Relativity models and that super-quintessence is not more than a mathematical outcome. Finally, in the case of non-minimally coupled theories with coupling $F=1+\xi \phi^2$ and tracking potentials, it is shown that no super-quintessence is possible. 
Diego F. Torres