  We derive here a robust bound on the effective number of neutrinos from
constraints on primordial nucleosynthesis yields of deuterium and helium. In
particular, our results are based on very weak assumptions on the astrophysical
determination of the helium abundance, namely that the minimum effect of
stellar processing is to keep constant (rather than increase, as expected) the
helium content of a low-metallicity gas. Using the results of a recent analysis
of extragalactic HII regions as upper limit, we find that Delta Neff<= 1 at 95
% C.L., quite independently of measurements on the baryon density from cosmic
microwave background anisotropy data and of the neutron lifetime input. In our
approach, we also find that primordial nucleosynthesis alone has no significant
preference for an effective number of neutrinos larger than the standard value.
The ~2 sigma hint sometimes reported in the literature is thus driven by CMB
data alone and/or is the result of a questionable regression protocol to infer
a measurement of primordial helium abundance.
