Stars as Laboratories for Fundamental Physics - MPP Theory Group

258 Chapter 7
component Majorana neutrinos. In this language a four-component
Dirac neutrino consists of two degenerate two-component Majorana
ones with λ = +1 and −1 so that their contributions cancel exactly,
reproducing the absence of lepton number violation for Dirac neutrinos.
If one takes the largest cosmologically allowed value m ντ = 30 eV and
the largest experimentally allowed mixing amplitude (Sect. 8.2.4) of
|U e,3 | ≈ 0.16 one may have a contribution as large as 0.8 eV from ν τ .
7.1.5 Cosmological Mass Bounds
Cosmology arguably yields the most important neutrino mass bounds
(Kolb and Turner 1990; Börner 1992). In the framework of the big-bang
scenario of the early universe one expects about as many “blackbody
neutrinos” in the universe as there are cosmic microwave photons. In
detail, the cosmic energy density in massive neutrinos is found to be
3∑
ρ ν = 3 n 11 γ m i , (7.2)
i=1
with n γ the present-day density of microwave background photons and
m i the neutrino masses. In units of the cosmic critical density this is
Ω ν h 2 =
3∑
i=1
m i
93 eV , (7.3)
where h is the Hubble constant in units of 100 km s −1 Mpc −1 . The
observed age of the universe together with the measured expansion
rate yields Ωh 2 < ∼ 0.4 so that for any of the known families
m ν ∼ < 30 eV . (7.4)
If one of the neutrinos had a mass near this bound it would be the main
component of the long-sought dark matter of the universe.
Certain scenarios of structure formation currently favor “hot plus
cold dark matter” where neutrinos with m νe + m νµ + m ντ ≈ 5 eV play a
sub-dominant dynamical role but help to shape the required spectrum
of primordial density perturbations (Pogosyan and Starobinsky 1995
and references therein). Preferably, the three neutrino masses should
be degenerate rather than one dominating flavor.
If neutrinos were unstable and if they decayed so early that their
decay products were sufficiently redshifted by the expansion of the universe,
the cosmological mass bound can be violated without running
into direct conflict with observations. The excluded range of masses