Analysis of Dark Matter Decoupling Mechanism:Theoretical Derivation and Numerical Calculation from Thermal Equilibrium to Relic Abundance

Decoupling of dark matter can be understood through the Boltzmann equation and calculate how much dark matter will eventually remain in the universe. In the course of our study, the complete Boltzmann equation can be used, but given the more uniform distribution of matter in the early universe, some less important factors are ignored, such as the movement of particles in space and weak external forces. By changing the variables, Boltzmann equation can be turned into the Likati equation, which describes the strength and equilibrium properties of dark matter interactions. Through numerical calculations and approximation analysis, dark matter still maintains a thermal equilibrium when the temperature of the universe is high. But as the universe slowly cools, the rate of dark matter interaction does not keep up with the rate of the expansion of the universe, so that dark matter is separated from the thermal equilibrium, and eventually forms a stable residual amount of dark matter. The research linked the Boltzmann equation to the detachment process of dark matter, giving a reliable way to calculate the remaining amount of dark matter. However, there are some shortcomings in this study, such as assuming that the universe is completely homogeneous, considering only one way of interacting with dark matter. In later studies, we intend to add more real cosmic conditions and experimental data to improve the model, so that the nature of dark matter can be more accurately determined.