Weak Gravity Strongly Constrains Large-Field Axion Inflation

TL;DR

The article scrutinizes whether large-field inflation driven by compact axions can be consistent with quantum gravity. By systematically applying the Weak Gravity Conjecture to single- and multi-axion setups and introducing new conjectures—Single-EFT Consistency Criterion (SECC) and Extended Weak Gravity Conjecture (XWGC)—the authors derive parametric bounds that cap the inflaton range at or near the Planck scale for a wide class of models, including N-flation and kinetic/alignment scenarios. They show that magnetic WGC considerations, KK spectra, and monodromy constraints reinforce these bounds, and although some loopholes exist, they are tightly controlled by the proposed conjectures. The work significantly narrows the space of viable large-field axion inflation models and suggests a generic incompatibility with super-Planckian field ranges under these quantum gravity-inspired constraints.

Abstract

Models of large-field inflation based on axion-like fields with shift symmetries can be simple and natural, and make a promising prediction of detectable primordial gravitational waves. The Weak Gravity Conjecture is known to constrain the simplest case in which a single compact axion descends from a gauge field in an extra dimension. We argue that the Weak Gravity Conjecture also constrains a variety of theories of multiple compact axions including N-flation and some alignment models. We show that other alignment models entail surprising consequences for how the mass spectrum of the theory varies across the axion moduli space, and hence can be excluded if further conjectures hold. In every case that we consider, plausible assumptions lead to field ranges that cannot be parametrically larger than the Planck scale. Our results are strongly suggestive of a general inconsistency in models of large-field inflation based on compact axions, and possibly of a more general principle forbidding super-Planckian field ranges.

Figures (3)

• Figure 1: How the XWGC closes the small-action loophole when $\theta = \pi$. We depict the case $g_{\rm KK} = 1$ for convenience. The horizontal axis is the charge-to-mass ratio $z$ for the $U(1)$ gauge group giving rise to the axion. The vertical axis is the charge-to-mass ratio for Kaluza-Klein charge. The points on the vertical axis (orange circles) correspond to graviton KK modes. The points off the axis (blue squares) correspond to charged particle KK modes, which as $n \to \infty$ accumulate near the orange points. We see that the convex hull condition demands that the horizontal coordinate $z_1$ at $n = 1$ be $\geq 1$, leading to the bound $f < \frac{\sqrt{\gamma}}{\pi} M_{\rm Pl}$.
• Figure 2: Two views of the fundamental domain (shaded) of the two axions for the case $N = 5$, together with a trajectory (thick blue arrow) beginning at a maximum of the potential and ending at the origin. For clarity, the view on the left and right are not drawn to the same scale. The right hand view is a "natural" parametrization with $0 \leq \theta_{A,B} \leq 2\pi$ but requires that we discontinuously change the value of $\theta$ and execute a corresponding monodromy on the Kaluza--Klein spectrum when wrapping around the torus. The left-hand view chooses a parametrization in which the values of $\theta_{A,B}$ and the Kaluza-Klein masses change smoothly during all of inflation. To illustrate the periodic identifications imposed on the boundaries, we show two points labeled with a red $\color{red} \circ$ that are identified and two points labeled with a purple $\color{purple} \times$ that are identified.
• Figure 3: Kaluza--Klein mode spectrum for a particle of charge $q = 11$ with an $N$-site lattice regulator for multiple choices of $N$. Blue curves are $N = 4$; purple, $N = 9$; red, $N = 28$; and orange, the continuum result $N \to \infty$. Observe that the spectrum of low-lying modes at $mR \stackrel{<}{{}_\sim} 1$ is the same for any number of lattice sites. However, the behavior of an individual mode tracked as $\theta$ is continuously varied is dramatically different at small $N$ and large $N$. The solid lines are modes with zero mass at the origin of moduli space, and the dashed lines are modes with zero mass at $\frac{\theta}{2\pi} = \frac{10}{11}$. Faint curves in the background show the other modes.