Double Exponents in $SL(2,\mathbb{Z})$ Cosmology

TL;DR

This paper investigates $SL(2, obreak ext{Z})$ invariant $ ext{alpha}$-attractor inflation models, revealing that the axion field remains nearly massless during inflation due to double-exponentially suppressed potential slopes, ensuring stability against quantum fluctuations.

Contribution

The study demonstrates the stability of inflationary trajectories in $SL(2, obreak ext{Z})$ invariant models and analyzes isocurvature perturbations and their potential transfer post-inflation.

Findings

Axion remains nearly massless during inflation.

Inflationary trajectory is stable against quantum fluctuations.

Isocurvature perturbations do not convert into curvature perturbations during inflation.

Abstract

Recently proposed $SL(2,\mathbb{Z})$ invariant $\alpha$-attractor models have plateau potentials with respect to the inflaton and axion fields. The slope of the potential in the inflaton direction is exponentially suppressed at large values of the inflaton field, but the slope of the potential in the axion direction is double-exponentially suppressed. Therefore, the axion field remains nearly massless and practically does not change during inflation. The inflationary trajectory in such models is stable with respect to quantum fluctuations of the axion field. We show that isocurvature perturbations do not feed into the curvature perturbations during inflation, and discuss the possibility of such transfer at the post-inflationary stage.