Dark Matter as a Non-Relativistic Bose-Einstein Condensate with Massive Gravitons

Abstract: We confront a non-relativistic Bose--Einstein Condensate (BEC) model of light bosons interacting gravitationally either through a Newtonian or a Yukawa potential with the observed rotational curves of $12$ dwarf galaxies. The baryonic component is modelled as an axisymmetric exponential disk and its characteristics are derived from the surface luminosity profile of the galaxies. The purely baryonic fit is unsatisfactory, hence a dark matter component is clearly needed. The rotational curves of five galaxies could be explained with high confidence level by the BEC model. For these galaxies, we derive: (i) upper limits for the allowed graviton mass; and (ii) constraints on a velocity-type and a density-type quantity characterizing the BEC, both being expressed in terms of the BEC particle mass, scattering length and chemical potential. The upper limit for the graviton mass is of the order of $10^{-26}$ $\text{eV/c}^2$, three orders of magnitude stronger than the limit derived from recent gravitational wave detections.