We discuss the thermal evolution and Bose-Einstein condensation of ultra-light dark matter particles at finite, realistic cosmological temperatures. We find that if these particles decouple from regular matter before Standard model particles annihilate, their temperature will be about 0.9 K. This temperature is substantially lower than the temperature of CMB neutrinos and thus Big Bang Nucleosynthesis remains unaffected. In addition the temperature is consistent with WMAP 7-year+BAO+H0 observations without fine-tuning. We focus on particles of mass of $msim 10^{-23}$ eV, which have Compton wavelengths of galactic scales. Agglomerations of these particles can form stable halos and naturally prohibit small scale structure. They avoid over-abundance of dwarf galaxies and may be favored by observations of dark matter distributions. We present numerical as well as approximate analytical solutions of the Friedmann-Klein-Gordon equations and study the cosmological evolution of this scalar field dark matter from the early universe to the era of matter domination. Today, the particles in the ground state mimic presureless matter, while the excited state particles are radiation like.
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