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Is dark matter a BEC or scalar field?

This is a brief review on the history of the Bose-Einstein condensate (BEC) or boson star model of galactic dark matter halos, where ultra-light scalar dark matter particles condense in a single BEC quantum state. The halos can be described as a self-gravitating, possibly self-interacting, coherent scalar field. On a scale larger than galaxies, dark matter behaves like cold dark matter while below that scale the quantum mechanical nature suppresses the dark matter structure formation due to the minimum length scale determined by the mass $m\st{>}{\sim}10^{-24} eV$ and the self-interaction of the particles. This property could alleviate the cusp problem and missing satellite problems of the $Λ$CDM model. Furthermore, this model well reproduces the observed rotation curves of spiral and dwarf galaxies, which makes the model promising.