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 ~ 10³ 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 Mpbh≈ 1.9 M_ with a fraction f≈ 1.5× 10⁻² of the PBHs having a mass of Mpbh > 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.