Automorphic inflation

TL;DR

Automorphic inflation introduces a symmetry-based framework for inflationary models using automorphic functions, linking the inflaton's target space to continuous and discrete groups, and exemplifies this with modular inflation.

Contribution

It formulates a novel inflationary framework based on automorphic functions and symmetry groups, connecting inflation dynamics to mathematical structures like automorphic forms and modular groups.

Findings

Automorphic inflation naturally incorporates shift symmetry in large field inflation.

The $j$-inflation model exemplifies modular inflation within this framework.

The approach links inflationary dynamics to advanced mathematical structures.

Abstract

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 $\Gamma$. The dynamics of inflationary models is essentially determined by the choice of the pair $(G,\Gamma)$ and a function $\Phi$ on the group $G$ relative to $\Gamma$. Automorphic inflation provides a natural structure in which the shift symmetry of large field inflation arises as one of generators of $\Gamma$. The model of $j-$inflation is discussed as an example of modular inflation associated to the special linear group.