  A QCD axion with a time-dependent decay constant has been known to be able to
accommodate high-scale inflation without producing topological defects or too
large isocurvature perturbations on CMB scales. We point out that a dynamical
decay constant also has the effect of enhancing the small-scale axion
isocurvature perturbations. The enhanced axion perturbations can even exceed
the periodicity of the axion potential, and thus lead to the formation of
axionic domain walls. Unlike the well-studied axionic walls, the walls produced
from the enhanced perturbations are not bounded by cosmic strings, and thus
would overclose the universe independently of the number of degenerate vacua
along the axion potential.
