Revisiting Dark Matter Freeze-in and Freeze-out through Phase-Space
  Distribution
  We revisit dark-matter production through freeze-in and freeze-out by solving
the Boltzmann equations at the level of the phase-space distribution $f(p,t)$.
Using the $2\to2$ annihilation and the $1\to2$ decay processes for
illustration, we compare the resulting dark-matter relic abundance with that
from the number-density approach. In the transition regime between freeze-in
and freeze-out, we find the difference can be quite significant, or even by
orders of magnitude if the annihilation of dark-matter particles or the
decaying mediator is neglected. The freeze-in production in the $2\to2$ and the
$1\to 2$ processes can also result in non-thermal phase-space distributions, or
even multi-modal ones with out-of-equilibrium decay, which can potentially
affect structure formation at late times. We also investigate how elastic
scatterings can distort such non-thermal distributions.
