Spinodal Instabilities and Super-Planckian Excursions in Natural
  Inflation
  Models such as Natural Inflation that use Pseudo-Nambu-Goldstone bosons
(PNGB's) as the inflaton are attractive for many reasons. However, they
typically require trans-Planckian field excursions $\Delta \Phi>M_{\rm Pl}$,
due to the need for an axion decay constant $f>M_{\rm Pl}$ to have both a
sufficient number of e-folds {\em and} values of $n_s,\ r$ consistent with
data. Such excursions would in general require the addition of all other higher
dimension operators consistent with symmetries, thus disrupting the required
flatness of the potential and rendering the theory non-predictive. We show that
in the case of Natural Inflation, the existence of spinodal instabilities
(modes with tachyonic masses) can modify the inflaton equations of motion to
the point that versions of the model with $f<M_{\rm Pl}$ can still inflate for
the required number of e-folds. The instabilities naturally give rise to two
separate phases of inflation with different values of the Hubble parameter $H$
one driven by the zero mode, the other by the unstable fluctuation modes. The
values of $n_s$ and $r$ typically depend on the initial conditions for the zero
mode, and, at least for those examined here, the values of $r$ tend to be
unobservably small.
