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.Comment: latex. This version includes the figure as a compressed fig.uu file,
appended at the end. Moreover it adds a reference to the work of Chun, Kim
and Ki