Automorphic inflation

A framework of inflation is formulated based on symmetry groups and their associated automorphic functions. In this setting the inflaton multiplet takes values in a curved target space constructed from a continuous group G   and a discrete subgroup Γ. The dynamics of inflationary models is essentially determined by the choice of the pair (G,Γ)(G,Γ) and a function Φ on the group G. Automorphic inflation provides a natural structure in which the shift symmetry of large field inflation arises as one of generators of Γ. The model of j-inflation is discussed as an example of modular inflation associated with the special linear group.