Big Bang Nucleosynthesis; electron-photon ratio

Thread starter ergospherical
Start date May 18, 2024
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Electron Photon

May 18, 2024

ergospherical

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Homework Statement: See the image below!

Relevant Equations: N/A

I'm asking mainly about part (c). Within the context of BBN, I'm a little unsure how you account for different baryons (i.e. does ##n_b## include neutrons, protons, hydrogen and helium, given that helium itself contains both neutrons and protons?)

For completeness, for part (b) I would just use the non-relativistic number density expression for electrons (given that ##T < m_e##) and the relativistic one for photons:\begin{align*}
n_{e} &= 2\left( \frac{m_e T}{2\pi} \right)^{3/2} e^{-m_e/T} \\
n_{\gamma} &= \frac{2\zeta(3)}{\pi^2} T^3
\end{align*}and take the ratio.

So coming back to (c), we have derived elsewhere that ##n_{\mathrm{He}}/n_{\mathrm{H}} \sim 1/16##. What should I write for the baryon number ##n_b##? At this point I would have thought almost all neutrons be inside helium nuclei, but the question hints not to ignore terms of order ##n_n/n_p##.

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