Flavor versus mass eigenstates in neutrino asymmetries: implications for cosmology

Gabriela Barenboim,Wan-Il Park,William H Kinney

doi:10.1140/epjc/s10052-017-5147-4

Abstract

We show that, if they exist, lepton number asymmetries (L_alpha ) 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.

Highlights

If asymmetric neutrinos have a thermal distribution, their contribution to Neff is expressed as Neff = ξα 2+ ξα π π (1)where ξα ≡ μα/T is the neutrino degeneracy parameter
We argue that the equilibrium lepton number asymmetry matrix reached by the Big Bang Nucleosynthesis (BBN) epoch is diagonal in the mass-eigenstate basis and related to the one in the flavor-eigenstate basis by the Pontecorvo–Maki– Nakagawa–Sakata (PMNS) matrix, and we show that the lepton number asymmetries of the mass eigenstates are different from those of flavors
Constraints in the H0, ξ parameter space are extremely similar to the case of no tensors, which is reasonable considering the upper bound of r < 0.07 obtained from Planck + BICEP/Keck data [44]

Summary

Introduction

If asymmetric neutrinos have a thermal distribution, their contribution to Neff is expressed as. Due to neutrino flavor oscillations [9,10,11,12], the equilibrium density matrix is not diagonal in the flavor basis (as one naively expects, flavor eigenstates not being asymptotic states of the Hamiltonian) and their description in terms of only diagonal components (a more or less hidden assumption when assuming thermal distribution for flavors) cannot capture all the contributions to the extra radiation energy density [8]. In the very early universe, it is natural to assume that neutrinos are in interaction eigenstates (i.e., flavor eigenstates), since their kinematic phases are very small and collisional interactions to thermal bath are large enough to block flavor oscillations If it were generated at very high energy, Lf is likely to be diagonal and to remain constant.

Cosmological constraints

Case 1

Case 2