SUMMARY
The discussion centers on the relationship between weak interaction cross-sections and temperature in the early universe, specifically demonstrating that the rate of weak interactions, denoted as \(\sigma_{wk}\), is proportional to \(T^{5/2}\). The weak interaction coupling constant, \(g_{wk} \approx 1.4 \times 10^{49} \, \text{erg cm}^3\), is utilized in the formula \(\sigma_{wk} = g_{wk}^2 \left[ \frac{k_B T}{(\bar{h} c)^2} \right]^2\). The collision time, \(\tau_{coll} = \frac{1}{n \sigma_{wk} c}\), is identified as inversely related to the interaction rate, with the number density \(n\) being proportional to \(T^3\). This analysis confirms that in a radiation-dominated universe, the temperature directly influences the weak interaction rates.
PREREQUISITES
- Understanding of weak interaction physics and cross-sections
- Familiarity with thermodynamic concepts, particularly temperature and energy relations
- Knowledge of particle density and relativistic particle behavior
- Basic grasp of cosmological principles, including the scale factor and redshift
NEXT STEPS
- Explore the derivation of weak interaction cross-sections in particle physics
- Study the relationship between temperature and energy in cosmology
- Investigate the implications of radiation domination on particle interactions
- Learn about the Boltzmann distribution and its role in early universe conditions
USEFUL FOR
Physicists, cosmologists, and students studying particle interactions and the early universe dynamics will benefit from this discussion.