Effect of neutrino heating on primordial nucleosynthesis

We modify the standard code for primordial nucleosynthesis to include the effect of the slight heating of neutrinos by $e^{\pm }$ annihilations. There is a small, systematic change in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ yield, $\Delta Y\simeq +1.5\mathrm{}\times {10}^{-4\mathrm{}}$, which is insensitive to the value of the baryon-to-photon ratio $\eta$ for ${10}^{-10\mathrm{}}\lesssim \eta \lesssim {10}^{-9\mathrm{}}$. We also find that the baryon-to-photon ratio decreases by about 0.5% less than the canonical factor of $\frac{4}{11}$ because some of the entropy in $e^{\pm }$ pairs is transferred to neutrinos. These results are in accord with recent analytical estimates.