Precision prediction for the big-bang abundance of primordial4He

Abstract

Within the standard models of particle physics and cosmology we have calculated the big-bang prediction for the primordial abundance of ${}^{4}\mathrm{He}$ to a theoretical uncertainty of less than $0.1% (\ensuremath{\delta}{Y}_{P}l\ifmmode\pm\else\textpm\fi{}0.0002),$ improving the current theoretical precision by a factor of 10. At this accuracy the uncertainty in the abundance is dominated by the experimental uncertainty in the neutron mean lifetime, ${\ensuremath{\tau}}_{n}=885.4\ifmmode\pm\else\textpm\fi{}2.0 \mathrm{sec}.$ 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-$\ensuremath{\alpha}$ 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 designed to control numerical errors to be less than 0.1% . Our predictions for the ${}^{4}\mathrm{He}$ abundance are presented in the form of an accurate fitting formula. Summarizing our work in one number, ${Y}_{P}(\ensuremath{\eta}=5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10})=0.2462\ifmmode\pm\else\textpm\fi{}0.0004 (\mathrm{expt})\ifmmode\pm\else\textpm\fi{}l0.0002 (\mathrm{theory}).$ Further, the baryon density inferred from the Burles-Tytler determination of the primordial D abundance, ${\ensuremath{\Omega}}_{B}{h}^{2}=0.019\ifmmode\pm\else\textpm\fi{}0.001,$ leads to the prediction ${Y}_{P}=0.2464\ifmmode\pm\else\textpm\fi{}0.0005 (\mathrm{D}/\mathrm{H})\ifmmode\pm\else\textpm\fi{}l0.0002 (\mathrm{theory})\ifmmode\pm\else\textpm\fi{}0.0005 (\mathrm{expt}).$ This ``prediction'' and an accurate measurement of the primeval ${}^{4}\mathrm{He}$ abundance will allow an important consistency test of primordial nucleosynthesis.