If the dark matter in the universe is a self-gravitating Bose-Einstein condensate (BEC) with quartic self-interaction described by the stochastic Gross-Pitaevskii-Poisson system, the adhesion model, the Burgers equation and the cosmological Kardar-Parisi-Zhang (KPZ) equation that have been introduced heuristically to solve the problems inherent to cold dark matter (CDM) models find a natural justification and an interesting generalization.
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Pierre-Henri Chavanis (2011) studied this question.
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