A General Framework of Automorphic Inflation

TL;DR

This paper develops a comprehensive framework for automorphic inflation, integrating automorphic forms and representations to classify scalar field theories with rich symmetry structures, extending previous models like j-inflation.

Contribution

It introduces a general automorphic inflation framework, detailing the stratification of scalar theories via group and automorphic data, and generalizes j-inflation using Eisenstein series.

Findings

Framework unifies automorphic and modular inflation models

Classifies scalar theories by group and automorphic data

Extends j-inflation with Eisenstein series

Abstract

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.