Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>forest

The matter power spectrum at comoving scales of $(1\ensuremath{-}40){h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ 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-$\ensuremath{\alpha}$ 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 ${m}_{\mathrm{WDM}}\ensuremath{\gtrsim}550\text{ }\text{ }\mathrm{eV}$ ($2\ensuremath{\sigma}$) for early decoupled thermal relics and ${m}_{\mathrm{WDM}}\ensuremath{\gtrsim}2.0\text{ }\text{ }\mathrm{keV}$ ($2\ensuremath{\sigma}$) 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 ${m}_{3/2}\ensuremath{\lesssim}16\text{ }\text{ }\mathrm{eV}$ ($2\ensuremath{\sigma}$). This translates into a bound on the scale of supersymmetry breaking, ${\ensuremath{\Lambda}}_{\mathrm{susy}}\ensuremath{\lesssim}260\text{ }\text{ }\mathrm{TeV}$, for models of supersymmetric gauge mediation in which the gravitino is the lightest supersymmetric particle.