Bose-Einstein Condensate Cosmology within the Framework of QCD Axion

Bose-Einstein Condensation (BEC) cosmology is analyzed in the framework of a string-inspired axion model. The dispersion relation of the axionic mode includes both gravitational and self-interaction terms, the latter being small in magnitude but crucial for inducing instability of the condensate. The generation rate of BEC around redshift $z\approx 30$ is primarily governed by gravity, consistent with a phenomenological value $\mathrm{\Gamma }\approx {10}^{-31}$ eV adopted in previous work and realizable for the QCD axion. The relation between this early BEC epoch and the later formation of supermassive black holes at $z\approx 5$ is also discussed.