The simplest , “ standard ” model of Big Bang Nucleosynthesis ( SBBN ) assumes three light neutrinos ( N _ { \nu } = 3 ) and no significant electron neutrino asymmetry ( \nu _ { e } - \bar { \nu } _ { e } asymmetry parameter \xi _ { e } \equiv \mu _ { e } / kT , where \mu _ { e } is the \nu _ { e } chemical potential ) leaving only one adjustable parameter : the baryon to photon ratio \eta \equiv n _ { B } / n _ { \gamma } .
The primordial abundance of any one nuclide can , therefore , be used to measure \eta 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 , there is a tension between the SBBN-predicted helium-4 and lithium-7 abundances and their current , observationally inferred primordial abundances , suggesting that N _ { \nu } may differ from the standard model value of three and/or that \xi _ { e } 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 ( \eta , N _ { \nu } , and \xi _ { e } ) permitted by the data are quite small .
Within these ranges , the BBN-predicted abundances of D , ^ { 3 } He , ^ { 4 } He , and ^ { 7 } Li are very smooth , monotonic functions of \eta _ { 10 } , \Delta N _ { \nu } \equiv N _ { \nu } -3 , and \xi _ { e } .
As a result , it is possible to describe the dependencies 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 percent 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 to 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 .