Using $ΔN_{\rm eff}$ to constrain preferred axion model dark matter

Preferred axion models are minimal realizations of the Peccei-Quinn solution to the strong CP problem while providing a dark matter candidate. These models invoke new heavy quarks that interact strongly with the Standard Model bringing them into thermal equilibrium in the early Universe. We show that for a number of these models, the heavy quarks will decay after axions have decoupled from the Standard Model thermal bath. As a consequence, any axion products in the decay form a component of dark radiation. This provides the potential to differentiate between preferred axion models through measurements of the number of relativistic degrees of freedom. The most sensitive of which comes from the Planck collaboration's measurements of the Cosmic Microwave Background. We find that existing constraints allow us to rule out regions of parameter space for 40% of the canonical preferred axion models.