Extending preferred axion models via heavy-quark induced early matter domination

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.