Nonlinear axion dynamics and the formation of cosmological pseudosolitons

The (3+1)-dimensional evolution of an inhomogeneous axion field configuration around the QCD epoch is studied numerically, including important nonlinear effects due to the attractive self-interaction. It is found that axion perturbations on scales corresponding to causally disconnected regions at $T\sim 1$ GeV can lead to very dense pseudosoliton configurations we call axitons. These configurations evolve to axion miniclusters with a present density ${\rho }_a\gtrsim {10}^{-8\mathrm{}}$ g ${\mathrm{cm}}^{-3\mathrm{}}$. 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.