Probing oscillations into sterile neutrinos with cosmology, astrophysics and experiments

We perform a thorough analysis of oscillation signals generated by one extra sterile neutrino, extending previous analyses done in simple limiting cases and including the effects of established oscillations among active neutrinos. We consider the following probes: solar, atmospheric, reactor and beam neutrinos, big-bang nucleosynthesis (helium-4, deuterium), cosmic microwave background, large scale structure, supernovæ, neutrinos from other astrophysical sources. We find no evidence for a sterile neutrino in present data, identify the still allowed regions, and study which future experiments can best probe them: sub-MeV solar experiments, more precise studies of CMB or BBN, future supernova explosions, etc. We discuss how the LSND hint is strongly disfavoured by the constraints of (standard) cosmology.