Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 310 / 2 / c / Solution

Let $Y_{\mathrm{He}}\simeq 0.25$ be the present primordial helium mass fraction. If $n_{\mathrm{He}}$ is the helium-nucleus density and $n_H$ the hydrogen-nucleus density, thenSince $Y_{\mathrm{He}}=4n_{\mathrm{He}}/n_b$,This retains the correction from neutrons bound in helium. Charge neutrality requires one electron per proton, including bound electrons, so with the baryon-to-photon ratio $\eta =n_b/n_{\gamma }\simeq 6\times 10^{-10}$,