Split neutrinos, two Majorana and one Dirac, and implications for leptogenesis, dark matter, and inflation

We propose a simple framework to split neutrinos with a slight departure from tribimaximal-where two of the neutrinos are Majorana type which provide thermal leptogenesis. We propose a model based on S-3 flavor symmetry. The Dirac neutrino with a tiny Yukawa coupling explains primordial inflation and the cosmic microwave background radiation, where the inflaton is the gauge invariant flat direction. The observed baryon asymmetry, and the scale of inflation are intimately tied to the observed reactor angle sin theta(13), which can be further constrained by the LHC and the 0 nu beta beta experiments. The model also provides the lightest right-handed sneutrino as a part of the inflaton to be the dark matter candidate.