  We consider the possibility that thermalized dark-matter particles acquire
their mass thanks to the spontaneous breaking of a symmetry below some critical
temperature. We describe the regime where a freeze out mechanism takes place
shortly after the onset of the phase transition, while the dark-matter mass has
not yet reached its final constant value. For such a "spontaneous freeze out"
to yield the correct relic density, the present-time cross section of
annihilation of the dark matter into Standard-Model states has to be one or two
orders of magnitude larger than in the case of a constant dark-matter mass.
