  We discuss a model of dark matter consisting of high energy
anti-electron-neutrinos with leptonic force, which is produced by the conserved
leptonic charge $g_\ell$ associated with Lee-Yang's $U_1$ gauge symmetry. Based
on particle-cosmology for early universe, the high energy neutrino (HEN) model
of dark matter assumes that the neutron decay processes, $n\to p^+ + e^-
+\ov{\nu}_e$, dominate the epoch after the creation, collision and confinement
processes of quarks and antiquarks in the beginning. The HEN model implies the
following results: There are almost equal numbers of electrons, protons and
anti-electron-neutrinos dominated the matter cosmos. There are unobservable and
ubiquitous anti-electron-neutrinos $\ov{\nu}_e$ with leptonic charge $g_\ell$
in the universe. Although the total mass of anti-electron-neutrino dark matter
is negligible in the universe, its enhanced gravitational and leptonic forces
could lead to the observed flat rotation curves due to relativistic
$\ov{\nu}_e$, whose static force involves a factor $E_\nu/m_\nu\approx 10^6$.
We estimate the leptonic charge to be $g_\ell \approx 7 \times 10^{-21}$. The
model predicts that the anti-electron-neutrino dark matter can interact with
cosmic-ray protons to produce positrons, i.e. $\ov{\nu}_e + p^+ \to e^+ +n$,
through weak interaction of the unified electroweak theory. The
anti-electron-neutrino dark matter sheds light on the Alpha Magnetic
Spectrometer (AMS) experiment, which has detected the intriguing excess of
cosmic-ray positrons over what is expected. The HEN model of dark matter
suggests an experimental test of the new Lee-Yang force between electrons by
using modern precision Cavendish experiment.
