A robust upper limit on N_eff from BBN, circa 2011

TL;DR

This work derives a robust upper bound on the effective number of neutrinos, $N_{ m eff}$, using Big Bang Nucleosynthesis yields with minimal assumptions about the $^4$He abundance. By adopting a conservative treatment of $^4$He through measurements of nine metal-poor extragalactic H II regions and a non-decreasing helium evolution with metallicity ($dY/dZ \ge 0$), the authors construct a likelihood for the primordial $Y_p$ and combine it with deuterium priors and BBN yields computed with the code of Pisanti, anchoring the analysis with a CMB-derived baryon density $\omega_b h^2$. The resulting 1D likelihood, marginalized over $\omega_b$, shows that $\Delta N_{ m eff} \le 1$ at 95% CL across several data combinations, indicating no strong need for extra relativistic species and suggesting that CMB-only hints of additional radiation are not supported by BBN under these conservative assumptions. The study underscores the value of BBN–CMB synergy and anticipates Planck-era data to further sharpen constraints on $N_{ m eff}$, while acknowledging sensitivities to assumptions about helium evolution and neutron lifetime.

Abstract

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.

Figures (1)

• Figure 1: Marginalized 1-D likelihood functions $\cal L$ versus $N_{\rm eff}$ using the different combinations of data as in Table \ref{['tab1']}. Solid (red) and dashed (purple) curves are obtained using CMB measurement of $\omega_b$, with the dotted (black) one also adds CMB information on $Y_p$. In all cases the quite sharp cut-off at $N_{\rm eff} \sim 4$ is due to $^4$He abundance upper limit.