A Hamilton-Jacobi formulation of anisotropic inflation

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 β-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.