Cosmological particle freeze-out

Decoupling of a particle abundance from chemical equilibrium when interactions become too slow compared with cosmic expansion. Pair annihilation can continue after equilibrium production is negligible, leaving a nonzero relic abundance.

For $dY/dx=-\lambda Y^2/x^2$ after freeze-out, the exact limit is $Y_{\infty }=[Y_f^{-1}+\lambda /x_f{]}^{-1}$. The frequently used estimate $x_f/\lambda$ additionally neglects the initial inverse abundance.