Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
From Eq.(8.15), we can conclude, for example, that a positive chemical potential
for electron neutrinos (i.e. an excess of νe over ¯νe) would imply a decrease in the
neutron abundance which translates, in turn, into a decrease in the predicted 4 He
yield since in mass fraction, we have:
Xα ≈
2 (n/p)
. (8.16)
(n/p + 1)
Indeed, in the early Universe, alpha particles win the competition between entropy
and binding energy because the entropy per baryon is very high and alpha
particles have a binding per nucleon not very different from iron. At a
temperature Tα ∼ 100 keV, alpha particles form rapidly, incorporating almost
all neutrons. Therefore, the primordial 4 He yield is determined roughly by the
neutron-to-proton ratio n/p at Tα. The standard BBN 4 He mass fraction yield
prediction is (24.85 ± 0.05)% using the CMB anisotropy-determined baryon density
[40].
The idea we wish to explore is if distortions in the νe and ¯νe energy spectra
stemming from the CP-violating phase can alter lepton capture rates on nucleons
and thereby change n/p and the 4 He yield.
8.2 Neutrino flavor oscillations in the early universe
We study the effect of three-neutrino flavour oscillations on the process of neutrino
decoupling by solving the momentum-dependent kinetic equations for the
neutrino spectra. We also include the muon-antimuon interactions annihilation
whose presence is not negligible for our purpose: to study the effects of the CPviolating
phase on ξe and consequently on the neutron to proton ratio.
8.2.1 Theoretical framework
In order to study neutrino oscillations in the early universe we characterize the
neutrino ensemble in the usual way by generalized occupation numbers, i.e. by 3
× 3 matrices as described in appendix B. The form of the density matrices for a
mode with momentum p is
⎛
⎞
ρν(p, t) ≡ ⎝
ρνee ρνeµ ρνeτ
ρνµe ρνµµ ρνµτ
ρντe ρντµ ρνττ
⎠ (8.17)
Initially, the density matrix can be written as :
⎛
f(p, ξe) 0
ρν(p, t = 0) ≡ ⎝ 0 f(p, ξµ)
0
0
⎞
⎠ (8.18)
0 0 f(p, ξτ)
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