Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
where p denotes the neutrino momentum, T the temperature, and ξ the chemical
potential in units of T. A nonzero chemical potential results in extra energy
density,
ρrad =
1 + 7
8
4/3
4
Neff ργ
11
(8.5)
such that the effective number of neutrinos is increased from the standard model
prescription by
∆Nν = 30
2 ξ
+
7 π
15
4 ξ
7 π
(8.6)
The effective number of neutrino families Neff parametrizes the cosmic radiation
after e + e − annihilation. The standard value for Neff is 3.046, it deviates from
3 because of residual neutrino heating. Actually, large chemical potentials affect
BBN in two ways:
1. The extra energy density increases the expansion rate of the universe, thus
increasing the BBN helium abundance, and also alters CMB results. This sets
weak bound | ξα | 3, for all three flavours.
2. An additional, much stronger limit can be placed on the νe − νe asymmetry,
as it directly affects the neutron to proton ratio prior to BBN by altering
beta-equilibrium (n + νe ↔ p + e − and p + νe ↔ n + e + ). For example, positive
ξe increases the νe abundance relative to νe, thus lowering the neutron to proton
ratio and decreasing the helium yield. This sets the limit | ξe | 0.04. However,
it is possible that the two effects compensate for each other, i.e. the effects of a
small ξe are partially undone by an increased expansion rate due to a large ξµ,τ.
In this case the bounds become [82, 73]:
−0.01 < ξe < 0.22 (8.7)
| ξµτ |< 2.6 (8.8)
We now know that neutrinos oscillate, each individual lepton number Le, Lµ
and Lτ is violated and only the total lepton number is conserved. Since the mixing
angle are large enough, they can lead to equilibration of all flavours before
BBN. Therefore, if a large asymmetry is hidden in ξµ,τ it will transferred to ξe well
before freeze-out at T ≃ 1 MeV. Consequently, in such situation, the stringent
limit of BBN on ξe would apply to all flavours improving the bound on ξµ,τ [48].
8.1.2 The neutron to proton ratio
The neutron-to-proton ratio is set by the competition of the expansion rate of
the universe and the rates of the following lepton capture/decay processes:
νe + n ⇋ p + e − , (8.9)
137