Instabilities in neutrino systems induced by interactions with scalars
  If there are scalar particles of small or moderate mass coupled very weakly
to Dirac neutrinos, in a minimal way, then neutrino-anti-neutrino clouds of
sufficient number density can experience an instability in which helicities are
suddenly reversed. The predicted collective evolution is many orders of
magnitude faster than given by cross-section calculations. The instabilities
are the analogue of the ``flavor-angle" instabilities (enabled by the Z
exchange force) that may drive very rapid flavor exchange among the neutrinos
that emerge from a supernova. These exchanges do require a tiny seed in
addition to the scalar couplings, but the transition time is proportional to
the negative of the logarithm of the seed strength, so that the size of this
parameter is comparatively unimportant. For our actual estimates we use a tiny
non-conservation of leptons; an alternative would be a neutrino magnetic moment
in a small magnetic field. The possibility of a quantum fluctuation as a seed
is also discussed. Operating in the mode of putting limits on the coupling
constant of the scalar field, for the most minimal coupling scheme, with
independent couplings to all three $\nu$, we find a rough limit on the
dimensionless coupling constant for a neutrino-flavor independent coupling of
$G<10^{-10}$, to avoid the effective number of light neutrinos in the early
universe being essentially six. If, on the other hand, we wish to fine-tune the
model to give a more modest excess (over three) in the effective neutrino
number, as may be needed according to recent WMAP analyses, it is easy to do
so.
  \pacs{13.15.+g}
