Naturalness of nearly degenerate neutrinos

If neutrinos are to play a relevant cosmological role, they must be essenti ally degenerate. We study whether radiative corrections can or cannot be re sponsible for the small mass splittings, in agreement with all the availabl e experimental data. We perform an exhaustive exploration of the bimaximal mixing scenario, finding that (i) the vacuum oscillations solution to the s olar neutrino problem is always excluded; (ii) if the mass matrix is produc ed by a see-saw mechanism, there are large regions of the parameter space c onsistent with the large angle MSW solution, providing a natural origin for the Delta m(sol)(2) much less than Delta m(atm)(2) hierarchy; (iii) the bi maximal structure becomes then stable under radiative corrections. We also provide analytical expressions for the mass splittings and mixing angles an d present a particularly simple see-saw ansatz consistent with all observat ions. (C) 1999 Elsevier Science B.V. All rights reserved.