  Even though neutrinos and antineutrinos are everywhere in the Universe, their
critical importance might be overlooked, especially because that at least one
species of neutrinos has the mass 0.058 eV, far larger than the cosmic
thermalization temperature 1.9^\circ K. The non-zero mass makes neutrinos
participate the galaxy formation from the very beginning, in view of the
process of clustering. Unlike the cosmic microwave background (CMB), the cosmic
background neutrinos (CB\nu) cannot be uniform. Thus, we wish to examine the
questions such as: Is there some new source for neutrinos or antineutrinos,
that might be detectible experimentally? Is there some new interaction of
neutrinos with the visible world, that may be of numerical importance at, e.g.,
the ultra high energies (\ge 10^{13} eV)? One major conclusion is that, on the
basis of the Standard Model, neutrinos would eventually become the {\it only}
dark-matter species left in our Universe.
  Our Cosmos is limited in energy for various particles, electrons or photons
without threshold, while protons or neutrinos having the following hurdles to
overcome in reaching extreme energies such as 10^{18} eV. In an electron-rich
medium, the threshold is 10^{15} eV for an ultra high energy (UHECR) proton,
due to p + e^- \to n + \nu_e. On the other hand, the cosmic background
neutrinos would cut off UHECR neutrinos of greater than 10^{13} eV if at least
one kind of neutrinos has the mass 0.05 eV (as suggested by the experimental
value of 0.058 eV), due to \nu +{\bar \nu}_{CB} \to e^- + e^+; this, plus the
clustering due to mass, gives us some hope that this effect might be
detectible.
