# Chemical and Kinetic Equilibrium in Cosmology: Facts and Myths

## TL;DR

This paper clarifies that chemical and kinetic equilibrium are distinct processes in the early Universe, with different decoupling behaviors, emphasizing the importance of phase-space evolution for accurate cosmological predictions.

## Contribution

It provides a detailed analysis of the independence of chemical and kinetic equilibrium decouplings across various cosmological scenarios.

## Key findings

- Chemical and kinetic decouplings are independent processes.
- The order of decoupling is model-dependent.
- Phase-space evolution is crucial for robust predictions.

## Abstract

We clarify that chemical and kinetic equilibration in the early Universe are distinct: neither implies the other, and the ordering of their decouplings need not be universal. We illustrate this with Standard-Model neutrino decoupling, strong-washout leptogenesis, dark-matter scenarios where kinetic decoupling precedes chemical freeze-out (resonant/forbidden, conversion/coannihilation, coscattering), and dark sectors at with temperatures distinct from the visible-sector temperature, with semi-annihilation or 3 $\to$ 2 cannibal dynamics. The moral of the story is simple: Chemical equilibrium governs numbers, kinetic equilibrium governs shapes. In an expanding Universe the operators that control them rarely fade at the same time, and when they do not, the order of decoupling is model dependent. Turning to phase-space evolution whenever momentum selectivity matters is the surest way to obtain robust cosmological predictions.