Precision prediction for the big-bang abundance of primordial4He

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 $0.1\%\hspace{0.5em}(\delta Y_P<\pm 0.0002),$ 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, ${\tau }_n=885.4\mathrm{}\pm 2.0\hspace{0.5em}\sec .$ 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 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, $Y_P(\eta =5\mathrm{}\times {10}^{-10})=0.2462\mathrm{}\pm 0.0004\hspace{0.5em}\left(\mathrm{expt}\right)\pm <0.0002\mathrm{}\hspace{0.5em}\left(\mathrm{theory}\right).\mathrm{}$ Further, the baryon density inferred from the Burles-Tytler determination of the primordial D abundance, ${\Omega }_B{h}^2=0.019\mathrm{}\pm 0.001,$ leads to the prediction $Y_P=0.2464\mathrm{}\pm 0.0005\hspace{0.5em}(\mathrm{D}/\mathrm{H})\pm <0.0002\mathrm{}\hspace{0.5em}\left(\mathrm{theory}\right)\pm 0.0005\hspace{0.5em}\left(\mathrm{expt}\right).\mathrm{}$ This “prediction” and an accurate measurement of the primeval ${}^4\mathrm{He}$ abundance will allow an important consistency test of primordial nucleosynthesis.