Primordial nucleosynthesis for the new cosmology: Determining uncertainties and examining concordance

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) have a long history together in the standard cosmology. BBN accurately predicts the primordial light element abundances of deuterium, helium and lithium. The general concordance between the predicted and observed light element abundances provides a direct probe of the universal baryon density. Recent CMB anisotropy measurements, particularly the observations performed by the WMAP satellite, examine this concordance by independently measuring the cosmic baryon density. Key to this test of concordance is a quantitative understanding of the uncertainties in the BBN light element abundance predictions. These uncertainties are dominated by systematic errors in nuclear cross sections, however for helium-4 they are dominated by the uncertainties in the neutron lifetime and Newton’s G. We critically analyze the cross section data, producing representations that describe this data and its uncertainties, taking into account the correlations among data, and explicitly treating the systematic errors between data sets. The procedure transforming these representations into thermal rates and errors is discussed. Using these updated nuclear inputs, we compute the new BBN abundance predictions, and quantitatively examine their concordance with observations. Depending on what deuterium observations are adopted, one gets the following constraints on the baryon density: ${\Omega }_{\mathrm{B}}{h}^2=0.0229\mathrm{}\pm 0.0013$ or ${\Omega }_{\mathrm{B}}{h}^2{=0.0216\mathrm{}}_{-0.0021}^{+0.0020\mathrm{}}$ at 68% confidence, fixing $N_{\nu ,eff}=\mathrm{3.0.}\mathrm{}$ If we instead adopt the WMAP baryon density, we find the following deuterium-based constraints on the effective number of neutrinos during BBN: $N_{\nu ,eff}{=2.78\mathrm{}}_{-0.76}^{+0.87\mathrm{}}$ or $N_{\nu ,eff}{=3.65\mathrm{}}_{-1.30}^{+1.46\mathrm{}}$ at 68% confidence. Concerns over systematics in helium and lithium observations limit the confidence constraints based on this data provide. BBN theory uncertainties are dominated by the following nuclear reactions: ${d(d,n)\mathrm{}}^3\mathrm{He},$ $d(d,p)t,$ $d(p,\gamma {)}^3\mathrm{He},$ ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{He}{\mathrm{}(d,p)\mathrm{}}^4\mathrm{He}.$ With new nuclear cross section data, light element abundance observations and the ever increasing resolution of the CMB anisotropy, tighter constraints can be placed on nuclear and particle astrophysics.