ABSTRACT
Inclusion of a sterile neutrino particle in the Standard Model of electroweak theory also generates tiny active neutrino masses through a see-saw mechanism. Sterile neutrinos may be produced through active-sterile (να ↔ νs) neutrino oscillation. Sterile neutrinos of mass ∼ 100 eV can provide a warm dark matter (WDM) candidate as they have a free streaming length shorter than HDM and also partially solve the problem of large-scale structure formation. On the other hand, a preexisting lepton number asymmerty could serve as the ingredient in sterile neutrino production through a resonant MSW (MikheyevSmirnov-Wolfenstein) conversion of active neutrinos when the effective oscillation potential is a function of matter-antimatter asymmetry
An
and expressed as
V Lα ≈ 0.35GFT 3 [ L0 +2Lνα + ∑
β6=α Lνβ ] , (13.2)
with L0 denoting the contribution from the baryon asymmetry and elecron-positron asymmetry while Lνi (i ≡ α,β) is the asymmetry in the other active neutrino species νi. The adiabaticity condition favors the resonance production of sterile neutrinos and the contribution of sterile neutrino to matter density is
Ων ≈ F ( mνs
91.5h2 eV
) ≈ ( mνs
343eV
)( h 0.5
)−2(2Lνα +∑β6=α Lνβ 0.1
) ,
(13.3) where
F ≈ 4 3
∆Lνα (13.4) denotes the fraction of νs number density produced with respect to active neutrinos due to resonant conversion and ∆Lνα is the να ¯να asymmetry respectively, and h is the Hubble parameter. The adiabatic transition provides a different free streaming length,
λf.s. ∼ 40 ( mν
30eV
)−1(E/T 3.15
) Mpc. (13.5)
In this formalism, lepton asymmetry of about ∼ 10−3 to ∼ 10−1 for any of the active neutrino species will provide sterile neutrino dark matter of mass between ∼ 102 eV and ∼ 10 keV.
