Precision Prediction for the Big-Bang Abundance of Primordial Helium

Abstract

Within the standard models of particle physics and cosmology we have calculated the big-bang prediction for the primordial abundance of \he to a theoretical uncertainty of less than $0.1 \pct$ $(\delta Y_P<\pm 0.0002)$, 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, ${\tau }_n=885.4\pm 2.0sec$. 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\pct. Our predictions for the \EL[4]{He} abundance are presented in the form of an accurate fitting formula. Summarizing our work in one number, $Y_P(\eta =5\times 10^{-10})=0.2462\pm 0.0004(expt)\pm <0.0002(theory)$. Further, the baryon density inferred from the Burles-Tytler determination of the primordial D abundance, ${\Omega }_B{h}^2=0.019\pm 0.001$, leads to the prediction: $Y_P=0.2464\pm 0.0005(D/H)\pm <0.0002(theory)\pm 0.0005(expt)$. This ``prediction'' and an accurate measurement of the primeval \he abundance will allow an important consistency test of primordial nucleosynthesis.

Replaced fitting formulas - new versions differ by small but significant amount. Other minor changes. 30 pages, 17 figures, 5 tables

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