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Primordial black hole (PBH) formation during cosmic phase transitions andannihilation periods, such as the QCD transition or the $e^+e^-$-annihilation,is known to be particularly efficient due to a softening of the equation ofstate. We present a detailed numerical study of PBH formation during the QCDepoch in order to derive an accurate PBH mass function. We also brieflyconsider PBH formation during the $e^+e^-$-annihilation epoch. Ourinvestigation confirms that, for nearly scale-invariant spectra, PBH abundanceson the QCD scale are enhanced by a factor $\sim 10^3$ compared to a purelyradiation dominated Universe. For a power spectrum producing an (almost)scale-invariant PBH mass function outside of the transition, we find a peakmass of $M_{\rm pbh}\approx 1.9 M_{\odot}$ of which a fraction $f\approx1.5\times 10^{-2}$ of the PBHs have a mass of $M_{\rm pbh} > 10 M_{\odot}$,possibly contributing to the LIGO-Virgo black hole merger detections. We pointout that the physics of PBH formation during the $e^+e^-$-annihilation epoch ismore complex as it is very close to the epoch of neutrino decoupling. We arguethat neutrinos free-streaming out of overdense regions may actually hinder PBHformation.

Primordial black hole formation during the QCD phase transition: threshold, mass distribution and abundance