The cosmological axion domain wall problem

We revisit the domain wall problem for QCD axion models with more than
one quark charged under the Peccei- Quinn symmetry. Symmetry breaking
during or after inflation results in the formation of a domain wall
network which would cause cosmic catastrophe if it comes to dominate
the Universe. The network may be made unstable by invoking a ‘tilt’ in
the axion potential due to Planck scale suppressed non-renormalisable
operators. (Alternatively the random walk of the axion field during
inflation may generate a ‘bias’ favouring one of the degenerate
vacuua, but we find that this mechanism is irrelevant here.)
Consideration of the axion abundance generated by the collapse of the
wall network then requires the Peccei-Quinn scale to be rather low
(<5.4x10^8 GeV) – thus ruling out e.g. the DFSZ axion with mass below
11 meV, where most experimental searches are in fact focused.