Naturalness of nearly degenerate neutrinos

If neutrinos are to play a relevant cosmological role, they must be essentially degenerate. We study whether radiative corrections can or cannot be responsible for the small mass splittings, in agreement with all the available experimental data. We perform an exhaustive exploration of the bimaximal mixing scenario, finding that (i) the vacuum oscillations solution to the solar neutrino problem is always excluded; (ii) if the mass matrix is produced by a see-saw mechanism, there are large regions of the parameter space consistent with the large angle MSW solution, providing a natural origin for the Delta m^2_{sol} << Delta m^2_{atm} hierarchy; (iii) the bimaximal structure becomes then stable under radiative corrections. We also provide analytical expressions for the mass splittings and mixing angles and present a particularly simple see-saw ansatz consistent with all the observations.