We consider a cosmological scenario in which the very early Universe experienced a transient epoch of matter domination due to the formation of a large population of primordial black holes (PBHs) with masses $M lesssim 10^{9},textrm{g}$, that evaporate before Big Bang nucleosynthesis. In this context, Hawking radiation would be a non-thermal mechanism to produce a cosmic background of axion-like particles (ALPs). We assume the minimal scenario in which these ALPs couple only with photons. In the case of ultralight ALPs ($m_a lesssim 10^{-9},textrm{eV}$) the cosmic magnetic fields might trigger ALP-photon
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