Big Bang Nucleosynthesis; electron-photon ratio

Thread starter ergospherical
Start date May 18, 2024
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Electron Photon

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SUMMARY

The discussion focuses on the calculation of baryon number density in the context of Big Bang Nucleosynthesis (BBN), specifically addressing the inclusion of different baryons such as neutrons, protons, hydrogen, and helium. The user seeks clarification on whether the baryon number density, denoted as ##n_b##, should account for the contributions of these particles, particularly given the established ratio of helium to hydrogen nuclei as ##n_{\mathrm{He}}/n_{\mathrm{H}} \sim 1/16##. The user also references the non-relativistic and relativistic expressions for electron and photon number densities, respectively, to derive the electron-photon ratio.

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Understanding of Big Bang Nucleosynthesis (BBN)
Familiarity with baryon number density calculations
Knowledge of non-relativistic and relativistic statistical mechanics
Basic concepts of particle physics, specifically neutrons and protons

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Research the implications of baryon number density in cosmology
Study the derivation of the helium to hydrogen ratio in BBN
Learn about the role of neutrons and protons in nucleosynthesis
Explore the mathematical treatment of relativistic and non-relativistic particles

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Astronomers, cosmologists, and physicists interested in the early universe and the processes of nucleosynthesis, as well as students studying particle physics and cosmology.

May 18, 2024

ergospherical

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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##.