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 ∼ 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≈ 1.9 M_⊙ with a fraction f≈ 1.5× 10^-2 of the PBHs having a mass of M_ pbh > 10 M_⊙, 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.