Can Gravitational Instantons Really Constrain Axion Inflation?

TL;DR

This paper investigates whether gravitational instantons significantly generate scalar potentials that could challenge axion-based inflation models, concluding that their effects are surprisingly small even in string theory UV completions.

Contribution

It provides a model-independent analysis of gravitational instantons' impact on axion potentials, including detailed calculations and considerations of moduli stabilization and the Weak Gravity Conjecture.

Findings

Gravitational instantons induce a small scalar potential effect.

Explicit calculations show wormholes do not significantly contribute to the potential.

The effect remains small even at the highest string theory scales.

Abstract

Axions play a central role in inflationary model building and other cosmological applications. This is mainly due to their flat potential, which is protected by a global shift symmetry. However, quantum gravity is known to break global symmetries, the crucial effect in the present context being gravitational instantons or Giddings-Strominger wormholes. We attempt to quantify, as model-independently as possible, how large a scalar potential is induced by this general quantum gravity effect. We pay particular attention to the crucial issue which solutions can or cannot be trusted in the presence of a moduli-stabilisation and a Kaluza-Klein scale. An important conclusion is that, due to specific numerical prefactors, the effect is surprisingly small even in UV-completions with the highest possible scale offered by string theory. As we go along, we discuss in detail Euclidean wormholes, cored and extremal instantons, and how the latter arise from 5d Reissner-Nordstrom black holes. We attempt to dispel possible doubts that wormholes contribute to the scalar potential by an explicit calculation. We analyse the role of stabilised dilaton-like moduli. Finally, we argue that Euclidean wormholes may be the objects satisfying the Weak Gravity Conjecture extended to instantons.