Universality for quintessence

Several recent works suggested the possibility of describing inflation by means of a renormalization group equation. In this paper we discuss the application of these methods to models of quintessence. In this framework a period of exponential expansion corresponds to the slow evolution of the scalar field in the neighborhood of a fixed point. A minimal set of universality classes for models of quintessence is defined and the transition from a matter dominated to quintessence dominated universe is studied. Models in which quintessence is non-minimally coupled with gravity are also discussed. We show that the formalism proves to be extremely convenient to describe quintessence and moreover we find that in most of the models discussed in this work quintessence naturally takes over ordinary matter.