Cosmic Four-Fermion Neutrino Secret Interactions, Enhancement and Total
  Cross Section
  The scattering of neutrinos assuming a "secret" interaction at low energy is
considered. To leading order in energy, the two-body potential is a
$\delta$-potential, and it is used as a motivation to study generic short-range
elastic interactions between neutrinos. The scattering cross section and
Sommerfeld enhancement depend on two phenomenological parameters deriving from
the exact form of the potential, akin to "renormalized" coupling constants.
Repulsive potentials lead to a decrease in the total cross section, resulting
in an enhancement of the neutrino density. For attractive potentials of the
right form, substantial Sommerfeld enhancement can appear.
