Cosmological Perturbations of Extreme Axion in the Radiation Era

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.