Constraints on Early Dark Energy from the Axion Weak Gravity Conjecture

A popular proposal for resolving the Hubble tension involves an early phase of dark energy, driven by an axion field with a periodic potential. In this paper, we argue that these models are tightly constrained by the axion weak gravity conjecture: for typical parameter values, the axion decay constant must satisfy $f < 0.008 M_{\textrm{Pl}}$, which is smaller than the axion decay constants appearing in the vast majority of early dark energy models to date. We discuss possible ways to evade or loosen this constraint, arguing that its loopholes are small and difficult to thread. This suggests that it may prove challenging to realize early dark energy models in a UV complete theory of quantum gravity.