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We show that when the QCD axion is directly coupled to quarks with $c_q/f \,\partial_\mu a \, \bar{q} \gamma^\mu \gamma^5 q$, such as in DFSZ models, thedominant production mechanism in the early universe at temperatures $1 \, {\rmGeV}\lesssim T \lesssim 100 \,{\rm GeV}$ is obtained via $q \bar{q}\leftrightarrow g a$ and $q g \leftrightarrow q a$, where $g$ are gluons.Different heavy quarks $q_i$ can produce a thermal axion background thatdecouples at a temperature $T_i$: (1) top quark at $T_t \lesssim 100 \, {\rmGeV}$ for $f/c_t \lesssim 3\times 10^8 {\rm GeV}$; (2) bottom quark at $T_b\lesssim m_b$, for $f/c_b\lesssim 8\times 10^{7} {\rm GeV}$; (3) charm quark at$T_c \lesssim m_c $ for $f/c_c \lesssim 5\times 10^{7} {\rm GeV}$. Each ofthese cases corresponds to a contribution to the effective number ofrelativistic degrees of freedom, in the windows given by $0.027 \leq \DeltaN_\text{eff}\leq 0.031$, $0.037 \leq \Delta N_\text{eff} \leq 0.039$ and $0.039\leq \Delta N_\text{eff}$, respectively. These contributions are larger thanthe one obtained when thermalization happens only above the electroweak phasetransition, $\Delta N_{\rm eff}\lesssim 0.027$, and are within reach of futureCMB S4 experiments, thus opening an alternative window to detect the axion andto test the early universe at such temperatures.

Observable windows for the QCD axion through $N_\text{eff}$