  We examine the cosmological consequences of the heavy quarks in KSVZ-type
axion models. We find that their presence often causes an early matter
domination phase, altering the evolution of the Universe. This extends the
axion mass into the region where standard cosmology leads to overproduction,
and allows for a greater number of axion models with non-renormalizable terms
to be viable. Quantitatively, we find that decays proceeding through effective
terms of up to dimension 9 ($d=9$) remain consistent with cosmological
constraints, in contrast with the result $d\leq5$ previously found in the
literature. As a consequence, the heavy quarks can be much heavier and the
axion mass window with the correct relic density for dark matter is extended by
orders of magnitude, down to $m_a\approx 6\times 10^{-9} \,{\rm eV}$. This is
achieved without resorting to fine-tuning of the initial misalignment angle,
bolstering the motivation for many future axion haloscope experiments.
Additionally, we explore how these models can be probed through measurements of
the number of relativistic degrees of freedom at recombination.
