Do observations prove that cosmological neutrinos are thermally distributed?

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.