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.
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