  Neutrino oscillations in the early Universe prior to the epoch of primordial
nucleosynthesis is studied by implementing real time non-equilibrium field
theory methods. We focus on two flavors of Dirac neutrinos, however, the
formulation is general. We obtain the equations of motion for neutrino
wavepackets of either chirality and helicity in the plasma allowing for CP
asymmetry. Contributions non-local in space-time to the self-energy dominate
over the asymmetry for $T \gtrsim 3-5 \mathrm{MeV}$ if the lepton and neutrino
asymmetries are of the same order as the baryon asymmetry. We find a new
contribution which cannot be interpreted as the usual effective potential. The
mixing angles and dispersion relations in the medium depend on \emph{helicity}.
We find that resonant transitions are possible in the temperature range $ 10
\lesssim T \ll 100 \mathrm{MeV} $. Near a resonance in the mixing angle, the
oscillation time scale in the medium as compared to the vacuum is
\emph{slowed-down} substantially for small vacuum mixing angle. The time scale
of oscillations \emph{speeds-up} for off resonance high energy neutrinos for
which the mixing angle becomes vanishingly small. The equations of motion
reduce to the familiar oscillation formulae for negative helicity
ultrarelativistic neutrinos, but include consistently both the \emph{mixing
angle and the oscillation frequencies in the medium}. These equations of motion
also allow to study the dynamics of right handed as well as positive helicity
neutrinos.
