Abstract
Evolution of inhomogeneities in the axion field around the QCD epoch is studied numerically, including for the first time important nonlinear effects. It is found that perturbations on scales corresponding to causally disconnected regions at T\ensuremath{\sim}1 GeV can lead to very dense axion clumps, with present density ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}}$\ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}8}$ g ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. This is high enough for the collisional 2a\ensuremath{\rightarrow}2a process to lead to Bose-Einstein relaxation in the gravitationally bound clumps of axions, forming Bose stars.
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