  Primordial neutrino-antineutrino asymmetries can be constrained through
big-bang nucleosynthesis (BBN) relic abundances and cosmic microwave background
(CMB) anisotropies, both observables being sensitive to neutrino properties.
The latter constraint, which is due to gravitational effects from all neutrino
flavors, is very minute since it is at least quadratic in the asymmetries. On
the contrary, the constraints from primordial abundances presently dominate,
although these abundances are almost only sensitive to the electron flavor
asymmetry. It is generally assumed that neutrino asymmetries are sufficiently
averaged by flavor oscillations prior to BBN, which allows to constrain a
common primordial neutrino asymmetry at the epoch of BBN. This simplified
approach suffers two caveats that we deal with in this article, combining a
neutrino evolution code and BBN calculation throughout the MeV era. First,
flavor "equilibration" is not true in general, therefore an accurate dynamical
evolution of asymmetries is needed to connect experimental observables to the
primordial asymmetries. Second, the approximate averaging of asymmetries
through flavor oscillations is associated to a reheating of the primordial
plasma. It is therefore crucial to correctly describe the interplay between
flavor equilibration and neutrino decoupling, as an energy redistribution prior
to decoupling does not significantly alter the final effective number of
neutrino species' value. Overall, we find that the space of allowed initial
asymmetries is generically unbound when using currently available primordial
abundances and CMB measurements. We forecast constraints using future CMB
experiment capabilities, which should reverse this experimental misfortune.
