The effect of primordial fluctuations on neutrino oscillations

Recent work has shown that neutrino oscillations in matter can be greatly enhanced by flips between mass eigenstates if the medium is fluctuating with a period equal to the neutrino oscillation length. Here we investigate the effect of the primordial fluctuations on the neutrino oscillations in the early universe. We calculate the oscillation probability in the case of a general power law fluctuation spectrum and for a more realistic spectrum predicted by inflation. We also include the effect of the amplification of fluctuations resulting from the QCD phase transition. We find that there is a region of parameter space where this mechanism would be the dominant mechanism for producing sterile neutrinos. However this conclusion does not take account of the damping of fluctuations on the neutrino oscillation scale when the neutrinos decouple from the plasma. We find that this reduces the probability of flips between the mass eigenstates to an unobservable level.