BBN for pedestrians

Abstract

The simplest, 'standard' model of Big Bang nucleosynthesis (SBBN) assumes three light neutrinos (Nv = 3) and no significant electron neutrino asymmetry (ve - ve asymmetry parameter ξe ≡ ↓e/kT, where ↓e is the chemical potential of v e) leaving only one adjustable parameter: the baryon to photon ratio η ≡ nB/nγ. The primordial abundance of any one nuclide can, therefore, be used to measure η and the value derived from the observationally inferred primordial abundance of deuterium closely matches that from current non-BBN data, primarily from the WMAP survey. However, using this same estimate for η, there is a tension between the SBBN-predicted abundances of 4He and 7Li and their current, observationally inferred primordial abundances, suggesting that Nv may differ from the standard model value of three and/or that ξe may differ from zero (or, that systematic errors in the abundance determinations have been underestimated or overlooked). The differences are not large and the allowed ranges of the BBN parameters (η, Nv and ξe) permitted by the data are quite small. Within these ranges, the BBN-predicted abundances of D, 3He, 4He, and 7Li are very smooth, monotonic functions of η10, ΔkNv ≡ Nv - 3 and ξe. As a result, it is possible to describe the dependence of these abundances (or powers of them) upon the three parameters by simple, linear fits which, over their ranges of applicability, are accurate to a few per cent or even better. The fits presented here have not been maximized for their accuracy but, rather, for their simplicity. To identify the ranges of applicability and relative accuracies, they are compared with detailed BBN calculations; their utility is illustrated with several examples. Given the tension within BBN, these fits should prove useful in facilitating studies of the viability of various options for non-standard physics and cosmology, prior to undertaking detailed BBN calculations.