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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 $(G,Γ)$ and a function $Φ$ on the group $G$ relative to $Γ$. 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 to the special linear group.