  Automorphic inflation is an application of the framework of automorphic
scalar field theory, based on the theory of automorphic forms and
representations. In this paper the general framework of automorphic and modular
inflation is described in some detail, with emphasis on the resulting
stratification of the space of scalar field theories in terms of the group
theoretic data associated to the shift symmetry, as well as the automorphic
data that specifies the potential. The class of theories based on Eisenstein
series provides a natural generalization of the model of $j$-inflation
considered previously.
