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.
