Constraints on dark matter particles from theory, galaxy observations and N-body simulations

Mass bounds on dark matter (DM) candidates are obtained for particles decoupling in or out of equilibrium with {\bf arbitrary} isotropic and homogeneous distribution functions. A coarse grained Liouville invariant primordial phase space density $ \mathcal D $ is introduced. Combining its value with recent photometric and kinematic data on dwarf spheroidal satellite galaxies in the Milky Way (dShps), the DM density today and $N$-body simulations, yields upper and lower bounds on the mass, primordial phase space densities and velocity dispersion of the DM candidates. The mass of the DM particles is bound in the few keV range. If chemical freeze out occurs before thermal decoupling, light bosonic particles can Bose-condense. Such Bose-Einstein {\it condensate} is studied as a dark matter candidate. Depending on the relation between the critical($T_c$)and decoupling($T_d$)temperatures, a BEC light relic could act as CDM but the decoupling scale must be {\it higher} than the electroweak scale. The condensate tightens the upper bound on the particle's mass. Non-equilibrium scenarios that describe particle production and partial thermalization, sterile neutrinos produced out of equilibrium and other DM models are analyzed in detail obtaining bounds on their mass, primordial phase space density and velocity dispersion. Light thermal relics with $ m \sim \mathrm{few} \mathrm{keV}$ and sterile neutrinos lead to a primordial phase space density compatible with {\bf cored} dShps and disfavor cusped satellites. Light Bose condensed DM candidates yield phase space densities consistent with {\bf cores} and if $ T_c\gg T_d $ also with cusps. Phase space density bounds from N-body simulations suggest a potential tension for WIMPS with $ m \sim 100 \mathrm{GeV},T_d \sim 10 \mathrm{MeV} $.
Comment: 27 pages 8 figures. Version to appear in Phys. Rev. D