Hypernatural inflation

TL;DR

This paper develops a supergravity-based inflation model combining dilaton and axion fields, with hyperbolic geometry enabling large axion decay constants, and explores its various inflationary regimes and initial condition solutions.

Contribution

It introduces a novel $ ext{alpha}$-attractor supergravity model with combined dilaton and axion fields, expanding the landscape of inflationary theories with large decay constants.

Findings

The model allows for exponentially large axion decay constants due to hyperbolic geometry.

It can describe multiple inflation regimes, including $ ext{alpha}$-attractor and natural inflation.

Generalized models can address initial condition problems for plateau potentials.

Abstract

We constructed a model of natural inflation in the context of $\alpha$-attractor supergravity, in which both the dilaton field and the axion field are light during inflation, and the inflaton may be a combination of the two. The T-model version of this theory is defined on the Poincare disk with radius |Z| = 1. It describes a Mexican hat potential with the flat axion direction corresponding to a circle of radius |Z| < 1. The axion decay constant $f_{a}$ in this theory can be exponentially large because of the hyperbolic geometry of the Poincare disk. Depending on initial conditions, this model may describe $\alpha$-attractor inflation driven by the radial component of the inflaton field, natural inflation driven by the axion field, or a sequence of these two regimes. We also construct the E-model version of this theory, which has similar properties. In addition, we describe generalized $\alpha$-attractor models where the potential can be singular at the boundary of the moduli space, and show that they can provide a simple solution for the problem of initial conditions for the models with plateau potentials.