Primordial black hole formation during the QCD phase transition. Threshold, mass distribution, and abundance

Primordial black hole (PBH) formation during cosmic phase transitions and annihilation periods, such as the QCD transition or the e(+)e(- )annihilation, is thought to be particularly efficient due to a softening of the equation of state. We present a detailed numerical study of PBH formation during the QCD epoch in order to derive an accurate PBH mass function. We also briefly consider PBH formation during the e(+)e(-)-annihilation epoch. Our investigation confirms that, for nearly scale-invariant spectra, PBH abundances on the QCD scale are enhanced by a factor similar to 10(3) compared to a purely radiation dominated Universe. For a power spectrum producing an (almost) scale-invariant PBH mass function outside of the transition, we find a peak mass of M-pbh approximate to 1.9M(circle dot) with a fraction f approximate to 1.5 x 10(-2) of the PBHs having a mass of M-pbh > 10M(circle dot), possibly contributing to the LIGO-Virgo black hole merger detections. We point out that the physics of PBH formation during the e+e--annihilation epoch is more complex as it is very close to the epoch of neutrino decoupling. We argue that neutrinos free-streaming out of overdense regions may actually hinder PBH formation.