Growing amount of data show evidence for statistical and apparent physical association between low-redshift galaxies and high-redshift quasi-stellar objects , suggesting noncosmological origin of their redshift and failure of classical quasar explanation .
Here we find an analytical solution of Einstein equations describing bubbles made from axions with periodic interaction potential .
Such particles are currently considered as one of the leading dark matter candidate .
The bubble interior has equal gravitational potential and , hence , photons emitted from the interior possess identical gravitational redshift .
The redshift depends on the bubble mass and can have any value between zero and infinity .
Quantum pressure supports the bubble against collapse and yields states stable on the scale of the Universe age .
Our results explain the observed quantization of quasar redshift and suggest that intrinsically faint point-like quasars associated with nearby galaxies ( a few % of known objects ) are axionic bubbles with masses 10 ^ { 8 } -10 ^ { 9 } M _ { \odot } and radii 10 ^ { 3 } -10 ^ { 4 } R _ { \odot } .
They are born in active galaxies and ejected into surrounding space .
Properties of such quasars unambiguously indicate presence of axion dark matter in the Universe and yield the axion mass m = 0.4 - 3 meV , which fits in the open axion mass window constrained by astrophysical and cosmological arguments .

We also found that tachyons , another dark matter candidate , can form objects with galactic size , negligible mass and any value of the gravitational redshift .
Such finding combined with quasar observations suggests that bright quasars 3C 48 , 3C 273 and 3C 279 are nuclei of forming nearby small galaxies embedded into tachyonic clots and possess pure gravitational redshift .
If the bright quasars later evolve into small companion galaxies , then their dark galactic halos , observed by rotation curves , are probably remnants of the tachyon matter .