Mass bounds on dark matter (DM) candidates are obtained for particles that decouple in or out of equilibrium while ultrarelativistic with arbitrary isotropic and homogeneous distribution functions. A coarse grained Liouville invariant primordial phase-space density $\mathcal{D}$ is introduced which depends solely on the distribution function at decoupling. The density $\mathcal{D}$ is explicitly computed and combined with recent photometric and kinematic data on dwarf spheroidal satellite galaxies in the Milky Way (dShps) and the observed DM density today yielding upper and lower bounds on the mass, primordial phase-space densities, and velocity dispersion of the DM candidates. Combining these constraints with recent results from $N$-body simulations yields estimates for the mass of the DM particles in the range of a few keV. We establish in this way a direct connection between the microphysics of decoupling in or out of equilibrium and the constraints that the particles must fulfill to be suitable DM candidates. If chemical freeze-out occurs before thermal decoupling, light bosonic particles can Bose condense. We study such Bose-Einstein condensate (BEC) as a dark matter candidate. It is shown that, depending on the relation between the critical ($T_c$) and decoupling ($T_d$) temperatures, a BEC light relic could act as cold DM but the decoupling scale must be higher than the electroweak scale. The condensate hastens the onset of the nonrelativistic regime and tightens the upper bound on the particle’s mass. A nonequilibrium scenario which describes particle production and partial thermalization, sterile neutrinos produced out of equilibrium, and other DM models is analyzed in detail and the respective bounds on mass, primordial phase-space density, and velocity dispersion are obtained. Thermal relics with $m\sim \mathrm{\text{few}}\mathrm{keV}$ that decouple when ultrarelativistic and sterile neutrinos produced resonantly or nonresonantly lead to a primordial phase-space density compatible with cored dShps and disfavor cusped satellites. Light Bose-condensed DM candidates yield phase-space densities consistent with cores and if $T_c\gg T_d$ also with cusps. Phase-space density bounds on particles that decoupled nonrelativistically combined with recent results from $N$-body simulations suggest a potential tension for WIMPs with $m\sim 100\mathrm{GeV}$, $T_d\sim 10\mathrm{MeV}$.

• Received 26 October 2007

DOI:https://doi.org/10.1103/PhysRevD.77.043518