  A QCD axion with a decay constant below $ 10 ^{ 11} ~{\rm GeV} $ is a
strongly-motivated extension to the Standard Model, though its relic abundance
from the misalignment mechanism or decay of cosmic defects is insufficient to
explain the origin of dark matter. Nevertheless, such an axion may still play
an important role in setting the dark matter density if it mediates a force
between the SM and the dark sector. In this work, we explore QCD axion-mediated
freeze-out and freeze-in scenarios, finding that the axion can play a critical
role for setting the dark matter density. Assuming the axion solves the strong
CP problem makes this framework highly predictive, and we comment on
experimental targets.
