Dark matter from an even lighter QCD axion: trapped misalignment
  We show that dark matter can be accounted for by an axion that solves the
strong CP problem, but is much lighter than usual due to a $Z_\mathcal{N}$
symmetry. The whole mass range from the canonical QCD axion down to the
ultra-light regime is allowed, with $3\le\mathcal{N}\lesssim65$. This includes
the first proposal of a "fuzzy dark matter" QCD axion with $m_a\sim10^{-22}$
eV. A novel misalignment mechanism occurs --{\it trapped misalignment}-- due to
the peculiar temperature dependence of the $Z_{\mathcal{N}}$ axion potential.
The dark matter relic density is enhanced because the axion field undergoes two
stages of oscillations: it is first trapped in the wrong minimum, which
effectively delays the onset of true oscillations. Trapped misalignment is more
general than the setup discussed here, and may hold whenever an extra source of
Peccei-Quinn breaking appears at high temperatures. Furthermore, it will be
shown that trapped misalignment can dynamically source the recently proposed
kinetic misalignment mechanism. All the parameter space is within tantalizing
reach of the experimental projects for the next decades. For instance, even
Phase I of CASPEr-Electric could discover this axion.
