  Classifying inflationary scenarios according to their scaling properties is a
powerful way to connect theory with observations. A useful tool to make such a
classification is the beta-function formalism. By describing inflation in terms
of renormalization group equations, within this framework, it is possible to
define universality classes, which can be considered as sets of theories that
share a common scale invariant limit. In this paper we apply the formalism to
define such classes of universality for models of inflation where the inflaton
is coupled to gauge fields. We show that the formalism may consistently be
extended to capture the peculiar features of these models such as statistical
anisotropy. We also obtain some consistency conditions which serve as useful
guidelines for model building.
