Primordial black holes with an accurate QCD equation of state

Abstract

Making use of definitive new lattice computations of the Standard Model thermodynamics during the quantum chromodynamic (QCD) phase transition, we calculate the enhancement in the mass distribution of primordial black holes (PBHs) due to the softening of the equation of state. We find that the enhancement peaks at approximately $0.7M_{\odot }$, with the formation rate increasing by at least two orders of magnitude due to the softening of the equation of state at this time, with a range of approximately $0.3M_{\odot }<M<1.4M_{\odot }$ at full width half-maximum. PBH formation is increased by a smaller amount for PBHs with masses spanning a large range, $10^{-3}{M}_{\odot }<M_{\mathrm{PBH}}<10^3{M}_{\odot }$, which includes the masses of the BHs that LIGO detected. The most significant source of uncertainty in the number of PBHs formed is now due to unknowns in the formation process, rather than from the phase transition. A near scale-invariant density power spectrum tuned to generate a population with mass and merger rate consistent with that detected by LIGO should also produce a much larger energy density of PBHs with solar mass. The existence of BHs below the Chandresekhar mass limit would be a smoking gun for a primordial origin and they could arguably constitute a significant fraction of the cold dark matter density. They also pose a challenge to inflationary model building which seek to produce the LIGO BHs without overproducing lighter PBHs.

18 pages, 5 figures. v2: Improvements in the presentation and references added, matches the published version

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