  It is usually assumed that relic neutrinos possess a Fermi-Dirac
distribution, acquired during thermal equilibrium in the Early Universe.
However, various mechanisms could introduce strong distortions in this
distribution. We perform a Bayesian likelihood analysis including the first
moments of the three active neutrino distributions as free parameters, and show
that current cosmological observations of light element abundances, Cosmic
Microwave Background (CMB) anisotropies and Large Scale Structures (LSS) are
compatible with very large deviations from the standard picture. We also
calculate the bounds on non-thermal distortions which can be expected from
future observations, and stress that CMB and LSS data alone will not be
sensitive enough in order to distinguish between non-thermal distortions in the
neutrino sector and extra relativistic degrees of freedom. This degeneracy
could be removed by additional constraints from primordial nucleosynthesis or
independent neutrino mass scale measurements.
