An Accurate Calculation of the Big-Bang Prediction for the Abundance of Primordial Helium

Within the standard model of particle physics and cosmology we have calculated the big-bang prediction for the primordial abundance of Helium to a theoretical uncertainty of $0.1 \pct$ $(\delta Y_P = \pm 0.0002)$. At this accuracy the uncertainty in the abundance is dominated by the experimental uncertainty in the neutron mean lifetime, $\tau_n = 885.3 \pm 2.0 \rm{sec}$. The following physical effects were included in the calculation: the zero and finite-temperature radiative, Coulomb and finite-nucleon mass corrections to the weak rates; order-$\alpha$ quantum-electrodynamic correction to the plasma density, electron mass, and neutrino temperature; and incomplete neutrino decoupling. New results for the finite-temperature radiative correction and the QED plasma correction were used. In addition, we wrote a new and independent nucleosynthesis code to control numerical errors to less than 0.1\pct. Our predictions for the \EL[4]{He} abundance are summarized with an accurate fitting formula. Summarizing our work in one number, $ Y_P(\eta = 5\times 10^{-10}) = 0.2460 \pm 0.0004 ({\rm expt}) \pm < 0.0002 ({\rm theory})$.