Leptogenesis and CPT violation

We construct a model in which neutrinos and anti-neutrinos acquire the same mass but slightly different energy dispersion relations. Despite CPT violation, spin-statistics is preserved. We find that leptogenesis can be easily explained within this model, without upsetting the solar, atmospheric and reactor neutrino data. Leptogenesis occurs without lepton-number violation and the non-equilibrium condition. We consider only three active Dirac neutrinos, and no new particles or symmetries are introduced.