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In a paper on Axions Peccei writes:

When the Universe goes through the PQ phase transition at $T ∼ f_a > > Λ_{QCD}$ the QCD anomaly is ineffective. As a result, early in the Universe $< a_{phys} >$ is arbitrary. Eventually, when the Universe cools down to temperatures of order $T \sim Λ_{QCD}$ the axion obtains a mass and $<a_{phys} >→ 0$. The PQ mechanism through which this happens, however, is not an instantaneous process and $< a_{phys} >$ oscillates to its final value. These coherent $p_a = 0$ axion oscillations contribute to the Universe’s energy density and axions act as cold dark matter.

He denotes by $a$ the axion field and $f_a$ the spontaneous PQ symmetry breaking energy scale.

Does he mean that in the early universe axions would be generated when the PQ symmetry is broken in a process analogous to reheating in inflation, or am I fully mistaken by this analogy?

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