Big Bang Nucleosynthesis; electron-photon ratio

Thread starter ergospherical
Start date May 18, 2024
Tags

Electron Photon

In summary, Big Bang Nucleosynthesis refers to the process that took place in the early universe, shortly after the Big Bang, where protons and neutrons combined to form light nuclei, predominantly hydrogen, helium, and trace amounts of lithium and beryllium. The electron-photon ratio during this period was crucial as it influenced the rate of nucleosynthesis and the formation of these elements. A high electron-photon ratio facilitated the combination of protons and neutrons, leading to the observed abundance of light elements in the universe today.

May 18, 2024

ergospherical

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##.

FAQ: Big Bang Nucleosynthesis; electron-photon ratio

What is Big Bang Nucleosynthesis?

Big Bang Nucleosynthesis (BBN) refers to the process that occurred within the first few minutes of the universe's existence, during which light elements were formed from protons and neutrons. This period is crucial for understanding the primordial abundances of elements like hydrogen, helium, and lithium, which were formed as the universe cooled and expanded after the Big Bang.

How does the electron-photon ratio affect Big Bang Nucleosynthesis?

The electron-photon ratio, which is the number of electrons to photons in the early universe, plays a significant role in BBN by influencing the temperature and density of the primordial plasma. A higher electron-photon ratio can lead to increased interactions among particles, affecting the rates of nuclear reactions that produce light elements during this epoch.

What is the significance of the predicted abundances of light elements?

The predicted abundances of light elements from BBN are significant because they provide a testable prediction of the Big Bang model. Observations of the cosmic microwave background radiation and the abundance of helium, deuterium, and lithium in the universe serve as critical evidence supporting the Big Bang theory, helping to confirm our understanding of the early universe's conditions.

How do scientists measure the electron-photon ratio?

Scientists measure the electron-photon ratio indirectly through observations of the cosmic microwave background radiation and the distribution of light elements in the universe. By analyzing the temperature fluctuations and polarization of the cosmic microwave background, researchers can infer the conditions of the early universe, including the electron-photon ratio at the time of nucleosynthesis.

What are the limitations of Big Bang Nucleosynthesis models?

Limitations of BBN models include uncertainties in nuclear reaction rates, the precise conditions during nucleosynthesis, and the effects of dark matter and neutrinos. Additionally, variations in the electron-photon ratio and other cosmological parameters can lead to discrepancies between predicted and observed abundances of light elements, necessitating further research and refinement of the models.