We discuss relaxation solutions to the dark matter-baryon coincidence problem in the context of QCD axion dark matter. In relaxation solutions, a moduli dynamically adjusts the mass of dark matter and baryons until their energy densities are $\mathcal{O}(1)$ the same. Because the QCD axion is heavily connected to QCD, scanning the QCD axion mass inherently also scans the proton mass. In the context of relaxation solutions, this implies that the ratio of dark matter to baryon abundances (${\mathrm{\Omega }}_{\mathrm{DM}}/{\mathrm{\Omega }}_{\mathrm{B}}$) is a ratio of beta functions showing that these models can only accommodate discrete values of ${\mathrm{\Omega }}_{\mathrm{DM}}/{\mathrm{\Omega }}_{\mathrm{B}}$ thereby “predicting” the ratio of the dark matter to baryon abundances. The original composite axion model has only a single integer degree of freedom $N$, the size of the gauge group, and we show that when $N=8$ the observed value of ${\mathrm{\Omega }}_{\mathrm{DM}}/{\mathrm{\Omega }}_{\mathrm{B}}=5.36$ is reproduced to within its percent level error bars. Novel tests of this model include more precise measurements of ${\mathrm{\Omega }}_{\mathrm{DM}}/{\mathrm{\Omega }}_{\mathrm{B}}$, a better lattice determination of the dependence of the proton mass on the high energy QCD gauge coupling, as well as more traditional tests such as fifth force experiments.

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• Axions
• Baryogenesis & leptogenesis
• Cosmology
• Phenomenology