Constraining Warm Dark Matter Candidates Including Sterile Neutrinos and Light Gravitinos with WMAP and the Lyman-alpha Forest

The matter power spectrum at comoving scales of (1-40)h-1 Mpc is very sensitive to the presence of Warm Dark Matter (WDM) particles with large free-streaming lengths. We present constraints on the mass of WDM particles from a combined analysis of the matter power spectrum inferred from the large samples of high-resolution high signal-to-noise Lyman-\u3b1 forest data of Kim et al. (2004) and Croft et al. (2002) and the cosmic microwave background data of WMAP. We obtain a lower limit of mWDM 73550 eV (2\u3c3) for early decoupled thermal relics and mWDM 732.0 keV (2\u3c3) for sterile neutrinos. We also investigate the case where in addition to cold dark matter a light thermal gravitino with fixed effective temperature contributes significantly to the matter density. In that case the gravitino density is proportional to its mass, and we find an upper limit m3/2 7216 eV (2\u3c3). This translates into a bound on the scale of supersymmetry breaking, \u39bsusy 72260 TeV, for models of supersymmetric gauge mediation in which the gravitino is the lightest supersymmetric particle