Primordial Black Holes from the QCD Transition?

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Can a violent process like sudden reheating after supercooling at the onset of a first-order QCD transition improve the possibility of primordial black hole formation? Underdensities reheat earlier than overdensities, there is a short period of huge pressure differences, hence fluid acceleration. Density perturbations on scales far below the Hubble radius λ≪ R H get an amplification which grows quadratically in wavenumber, the amplifications at the horizon scale are small. Primordial black hole formation cannot be sufficiently amplified by the QCD transition unless the initial spectrum is fine tuned.