Bounding axion dark energy

We study cosmological solutions of (pseudo)scalar theories with periodic potentials, in the presence of arbitrary cosmological fluids -- including a cosmological constant of either sign. Independently of the initial misalignment angle and field velocity, we derive an analytic bound that the axion mass parameter and decay constant fulfill as the universe decreases its acceleration rate, finding a natural application in models of thawing quintessence. As a first application, we illustrate the analytic handle our bound provides in bounding axion dark energy, after observational inputs from DESI and various supernovae data sets are taken into account. As a second application, we argue that our analytic bounds in combination with proposed quantum gravity constraints on axions exclude vast regions of parameter space. The combined constraints push the axion masses to be much larger than the Hubble scale, in tension with basic models of axion quintessence.