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

Abstract

Primordial black hole (PBH) formation during cosmic phase transitions and annihilation periods, such as the QCD transition or the ${e}^{+}{e}^{\ensuremath{-}}$ 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 ${e}^{+}{e}^{\ensuremath{-}}$-annihilation epoch. Our investigation confirms that, for nearly scale-invariant spectra, PBH abundances on the QCD scale are enhanced by a factor $\ensuremath{\sim}{10}^{3}$ 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 ${M}_{\mathrm{pbh}}\ensuremath{\approx}1.9{M}_{\ensuremath{\bigodot}}$ with a fraction $f\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ of the PBHs having a mass of ${M}_{\mathrm{pbh}}>10{M}_{\ensuremath{\bigodot}}$, possibly contributing to the LIGO-Virgo black hole merger detections. We point out that the physics of PBH formation during the ${e}^{+}{e}^{\ensuremath{-}}$-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.

Topics & Concepts