Intrinsically faint quasars: evidence for meV axion dark matter in the   Universe
  Growing amount of observations indicate presence of intrinsically faint quasar subgroup (a few % of known quasars) with noncosmological quantized redshift. 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 possesses equal gravitational redshift which can have any value between zero and infinity. Quantum pressure supports the bubble against collapse and yields states stable on the scale more then hundreds million years. Our results explain the observed quantization of quasar redshift and suggest that intrinsically faint point-like quasars associated with nearby galaxies are axionic bubbles with masses 10^8-10^9M_{Sun} and radii 10^3-10^4R_{Sun}. 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 \approx 1 meV, which fits in the open axion mass window constrained by astrophysical and cosmological arguments. 
Anatoly A. Svidzinsky