The lepton asymmetry: the last chance for a critical-density cosmology?

We use a wide range of observations to constrain cosmological models possessing a significant asymmetry in the lepton sector, which offer perhaps the best chance of reconciling a critical-density Universe with current observations. The simplest case, with massless neutrinos, fails to fit many experimental data and does not lead to an acceptable model. If the neutrinos have mass of order one electron-volt (which is favoured by some neutrino observations), then models can be implemented which prove a good fit to microwave anisotropies and large-scale structure data. However, taking into account the latest microwave anisotropy results, especially those from Boomerang, we show that the model can no longer accommodate the observed baryon fraction in clusters. Together with the observed acceleration of the present Universe, this puts considerable pressure on such critical-density models.