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Light scalars (as the axion) with mass m ~ 10^{-22} eV forming aBose-Einstein condensate (BEC) exhibit a Jeans length in the kpc scale and weretherefore proposed as dark matter (DM) candidates. Our treatment here isgeneric, independent of the particle physics model and applies to all DM BEC,in or out of equilibrium. Two observed quantities crucially constrain DM in aninescapable way: the average DM density rho_{DM} and the phase-space density Q.The observed values of rho_{DM} and Q in galaxies today constrain both thepossibility to form a BEC and the DM mass m. These two constraints robustlyexclude axion DM that decouples just after the QCD phase transition. Moreover,the value m ~ 10^{-22} eV can only be obtained with a number ofultrarelativistic degrees of freedom at decoupling in the trillions which isimpossible for decoupling in the radiation dominated era. In addition, we findfor the axion vacuum misalignment scenario that axions are produced stronglyout of thermal equilibrium and that the axion mass in such scenario turns to be17 orders of magnitude too large to reproduce the observed galactic structures.Moreover, we also consider inhomogenous gravitationally bounded BEC's supportedby the bosonic quantum pressure independently of any particular particlephysics scenario. For a typical size R ~ kpc and compact object masses M ~ 10^7Msun they remarkably lead to the same particle mass m ~ 10^{-22} eV as the BECfree-streaming length. However, the phase-space density for the gravitationallybounded BEC's turns to be more than sixty orders of magnitude smaller than thegalaxy observed values. We conclude that the BEC's and the axion cannot be theDM particle. However, an axion in the mili-eV scale may be a relevant source ofdark energy through the zero point cosmological quantum fluctuations.

Galaxy Phase-Space Density Data Preclude that Bose-Einstein Condensate be the Total Dark Matter