Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture

TL;DR

This paper explores how the weak gravity conjecture constrains large-field inflation models with many axions, showing that effective decay constant enhancement is limited unless models include many instantons or super-Planckian fields.

Contribution

It provides a comprehensive analysis of axion inflation models with multiple fields, deriving conditions under which decay constant enhancement is compatible with quantum gravity constraints.

Findings

Enhancement regimes include no, power-law, and exponential with respect to N.

WGC implies enhancement cannot grow parametrically with N for large N.

Models must have super-Planckian fields or many instantons to be consistent with quantum gravity.

Abstract

In this note, we discuss the implications of the weak gravity conjecture (WGC) for general models of large-field inflation with a large number of axions $N$. We first show that, from the bottom-up perspective, such models admit a variety of different regimes for the enhancement of the effective axion decay constant, depending on the amount of alignment and the number of instanton terms that contribute to the scalar potential. This includes regimes of no enhancement, power-law enhancement and exponential enhancement with respect to $N$. As special cases, we recover the Pythagorean enhancement of $N$-flation, the $N$ and $N^{3/2}$ enhancements derived by Bachlechner, Long and McAllister and the exponential enhancement by Choi, Kim and Yun. We then analyze which top-down constraints are put on such models from the requirement of consistency with quantum gravity. In particular, the WGC appears to imply that the enhancement of the effective axion decay constant must not grow parametrically with $N$ for $N \gg 1$. On the other hand, recent works proposed that axions might be able to violate this bound under certain circumstances. Our general expression for the enhancement allows us to translate this possibility into a condition on the number of instantons that couple to the axions. We argue that, at large $N$, models consistent with quantum gravity must either allow super-Planckian field excursions or have an enormous, possibly even exponentially large, number of dominant instanton terms in the scalar potential.