By combining data from cosmic microwave background (CMB) experiments (including the recent WMAP third year results), large scale structure (LSS) and Lyman-alpha forest observations, we constrain the hypothesis of a fourth, sterile, massive neutrino. For the 3 massless + 1 massive neutrino case we bound the mass of the sterile neutrino to m_s<0.26eV (0.44eV) at 95% (99.9%) c.l.. These results exclude at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. We then generalize the analysis to account for active neutrino masses (which tightens the limit to m_s<0.23eV 0.42eV) and the possibility that the sterile abundance is not thermal. In the latter case, the contraints in the (mass, density) plane are non-trivial. For a mass of >1eV or <0.05eV the cosmological energy density in sterile neutrinos is always constrained to be omega_nu <0.003 at 95 c.l.. However, for a sterile neutrino mass of ~0.25eV, omega_nu can be as large as 0.01.

5 pages, 3 figures; v2: update datasets to WMAP3, new Lyman Alpha, Baryonic oscillations; confidence limits tightened by a factor ~2, results unchanged; v3 minor changes, version accepted by PRL