  A number of proposed and ongoing experiments search for axion dark matter
with a mass nearing the limit set by small scale structure (${\cal O} ( 10 ^{ -
21 } {\rm eV} ) $). We consider the late universe cosmology of these models,
showing that requiring the axion to have a matter-power spectrum that matches
that of cold dark matter constrains the magnitude of the axion couplings to the
visible sector. Comparing these limits to current and future experimental
efforts, we find that many searches require axions with an abnormally large
coupling to Standard Model fields, independently of how the axion was populated
in the early universe. We survey mechanisms that can alleviate the bounds,
namely, the introduction of large charges, various forms of kinetic mixing, a
clockwork structure, and imposing a discrete symmetry. We provide an explicit
model for each case and explore their phenomenology and viability to produce
detectable ultralight axion dark matter.
