  Warm dark matter (WDM) means DM particles with mass m in the keV scale. For
large scales, (structures beyond ~ 100 kpc) WDM and CDM yield identical results
which agree with observations. For intermediate scales, WDM gives the correct
abundance of substructures. Inside galaxy cores, below ~ 100 pc, N-body WDM
classical physics simulations are incorrect because at such scales quantum WDM
effects are important. WDM quantum calculations (Thomas-Fermi approach) provide
galaxy cores, galaxy masses, velocity dispersions and density profiles in
agreement with the observations. For a dark matter particle decoupling at
thermal equilibrium (thermal relic), all evidences point out to a 2 keV
particle. Remarkably enough, sterile neutrinos decouple out of thermal
equilibrium with a primordial power spectrum similar to a 2 keV thermal relic
when the sterile neutrino mass is about 7 keV. Therefore, WDM can be formed by
7 keV sterile neutrinos. Excitingly enough, Bulbul et al. (2014) announced the
detection of a cluster X-ray emission line that could correspond to the decay
of a 7.1 keV sterile neutrino and to a neutrino decay mixing angle of \sin^2 2
\theta ~ 7 10^{-11} . This is a further argument in favour of sterile neutrino
WDM. Baryons, represent 10 % of DM or less in galaxies and are expected to give
a correction to pure WDM results. The detection of the DM particle depends upon
the particle physics model. Sterile neutrinos with keV scale mass (the main WDM
candidate) can be detected in beta decay for Tritium and Renium and in the
electron capture in Holmiun. The sterile neutrino decay into X rays can be
detected observing DM dominated galaxies and through the distortion of the
black-body CMB spectrum. So far, not a single valid objection arose against
WDM.
