Flavor versus mass eigenstates in neutrino asymmetries: implications for cosmology

We show that, if they exist, lepton number asymmetries (L_α) of neutrino flavors should be distinguished from the ones (L_i) of mass eigenstates, since Big Bang Nucleosynthesis (BBN) bounds on the flavor eigenstates cannot be directly applied to the mass eigenstates. Similarly., Cosmic Microwave Background (CMB) constraints on the mass eigenstates do not directly constrain flavor asymmetries. Due to the difference of mass and flavor eigenstates, the cosmological constraint on the asymmetries of neutrino flavors can be much stronger than the conventional expectation, but they are not uniquely determined unless at least the asymmetry of the heaviest neutrino is well constrained. The cosmological constraint on L_i for a specific case is presented as an illustration.