We present a model where an unstable MeV Majorana tau \neu can naturally reconcile the cold dark matter model (CDM) with cosmological observations of large and small scale density fluctuations and, simultaneously, with data on solar and atmospheric neutrinos. The solar \neu deficit is explained through long wavelength, so-called {\sl just-so} oscillations involving conversions of \ne into both \nm and a sterile species \ns, while atmospheric \neu data are explained through \nm to \ne conversions. Future long baseline \neu oscillation experiments, as well as some reactor experiments will test this hypothesis. The model is based on the spontaneous violation of a global lepton number symmetry at the weak scale. This symmetry plays a key role in generating the cosmologically required decay of the \nt with lifetime τντ∼102−104 seconds, as well as the masses and oscillations of the three light \neus \ne, \nm and \ns required in order to account for solar and atmospheric \neu data. It also leads to the invisibly decaying higgs signature that can be searched at LEP and future particle colliders.