The exact parity symmetric model and big bang nucleosynthesis
  The assumption of exact, unbroken parity symmetry leads directly to a simple predictive resolution of the atmospheric and solar neutrino puzzles. This is because the existence of this symmetry implies the existence of a set of mirror neutrinos which must mix maximally with the known neutrinos if neutrinos have mass. The maximal mixing of the electron neutrino with the mirror electron neutrino with $3 \times 10^{-10} eV^2 < |\delta m^2| < 10^{-3} eV^2$ eads to a predicted reduction of the solar neutrino flux by a factor of 2, which is in quite good agreement with the experiments. The maximal mixing of the muon neutrino with the mirror muon neutrino with $|\delta m^2| \simeq 10^{-2} eV^2$ also solves the atmospheric neutrino puzzle. We show that there is a significant range of parameters where these solutions are not in conflict with standard Big Bang Nucleosynthesis when the creation of lepton asymmetry due to neutrino oscillations is taken into account. 
R. Foot and R. R. Volkas