Introduction to Cosmology Ryden · Problem 9.2

The key insight is that $Y_{\max}$ (the maximum helium-4 mass fraction) is limited by how many neutrons can be produced and survive during Big Bang nucleosynthesis—which depends directly on the neutron–proton mass difference $Q_n$. A smaller $Q_n$ makes neutrons less energetically expensive to create, so more survive freeze-out and become available to build helium. Since each $^4$He nucleus needs 2 neutrons and 2 protons, you can estimate $Y_{\max}$ from the neutron abundance at freeze-out, which scales with $\exp(-Q_n/k_B T)$.

The key insight is that $Y_{\max}$ (the maximum helium-4 mass fraction) is limited by how many neutrons can be produced and survive during Big Bang nucleosynthesis—which depends directly on the neutron–proton mass difference $Q_n$. A smaller $Q_n$ makes neutrons less energetically expensive to create, so more survive freeze-out and become available to build helium. Since each $^4$He nucleus needs 2 neutrons and 2 protons, you can estimate $Y_{\max}$ from the neutron abundance at freeze-out, which scales with $\exp(-Q_n/k_B T)$.