  Sub-horizon perturbations under the extreme initial condition of the axion
model are investigated, where initial axion angles start near the potential
maximum. This work focuses on a few new features found in the extreme axion
model but absent in the free-particle model. A particularly novel new feature
is the spectral excess relative to the CDM model in some wave number range,
where the excess may be so large that landscapes of high-redshift universe
beyond $z=10$ can be significantly altered. For axions of particle mass
$10^{-22}$ eV, this range of wave number corresponds to first galaxies of few
times $10^9-10^{10} M_\odot$. We demonstrate that sub-horizon perturbations are
accurately described by Mathieu's equation and subject to parametric
instability, which explains this novel feature. Actually the axion model is not
a special one; perturbations in a wide range of scalar field models can share
the similar characteristic.
