  The companion-axion model introduces a second QCD axion to rescue the
Peccei-Quinn solution to the strong-CP problem from the effects of colored
gravitational instantons. As in single-axion models, the two axions predicted
by the companion-axion model are attractive candidates for dark matter. The
model is defined by two free parameters, the scales of the two axions' symmetry
breaking, so we can classify production scenarios in terms of the relative
sizes of these two scales with respect to the scale of inflation. We study the
cosmological production of companion-axion dark matter in order to predict
windows of preferred axion masses, and calculate the relative abundances of the
two particles. Additionally, we show that the presence of a second axion solves
the cosmological domain wall problem automatically in the scenarios in which
one or both of the axions are post-inflationary. We also suggest unique
cosmological signatures of the companion-axion model, such as the production of
a $\sim$10 nHz gravitational wave background, and $\sim 100\,M_\odot$
primordial black holes.
