Baryogenesis from primordial tensor perturbations

During inflation primordial quantum fluctuations of the spacetime metric become classical and there is a spontaneous CPT violation by the spin connection coupling terms of the metric with fermions. The energy levels of the left and the right chirality neutrinos is split which gives rise to a net lepton asymmetry at equilibrium. A net baryon asymmetry of the same magnitude can be generated from this lepton asymmetry either by a GUT, $B-L$ symmetry or by electroweak sphaleron processes which preserve $B+L$ symmetry. If the amplitude of the primordial tensor perturbations is of the order of $10^{-6}$ (as is expected from inflation models) and the lepton/baryon number violating processes freeze out at the GUT era $T_d \sim 10^{16} Gev$ then a baryon number asymmetry of the correct magnitude $10^{-10}$ can be generated.