Once popular several years ago, cosmologies with massive neutrinos as the dominant mass component1-4 were shown to suffer from several serious deficiencies. Foremost among the problems was the large clustering length predicted for matter and for galaxies, if they formed in regions of caustic surfaces5-8. It was argued that this problem could be circumvented if galaxies formed perferendally in low density regions of space, that is, if the galaxy distribution were anti-biased relative to the mass9-10. But further study11 showed that even if a working form of anti-biasing were found to alleviate the 'length scale problem' of galaxy formation, hot gas confined within the rich neutrino clusters would produce copious X-ray emission. The expected sizes, number density, temperatures and luminosities of these clusters would be in disagreement with observational data, unless only a very small fraction of the universe was in baryons, Ωb<~0.025, and the universe was quite young, h ~ 1 where H0 = 100 h km s-1 Mpc-1.