Non-Linear Axion Dynamics and Formation of Cosmological Pseudo-Solitons

The $(3+1)$-dimensional evolution of an inhomogeneous axion field configuration around the QCD epoch is studied numerically, including important non-linear effects due to the attractive self-interaction. It is found that axion perturbations on scales corresponding to causally disconnected regions at $T\sim 1\mathrm{G}\mathrm{e}\mathrm{V}$ can lead to very dense pseudo-soliton configurations we call axitons. These configurations evolve to axion miniclusters with present density ${\rho }_a\text{ga}{10}^{-8}\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$. This is high enough for the collisional $2a\to 2a$ process to lead to Bose–Einstein relaxation in the gravitationally bound clumps of axions, forming Bose stars.