ar X iv : a st ro - p h / 98 01 16 3 v 1 1 6 Ja n 19 98 ETH - TH / 98 - 01 PRIMORDIAL BLACK HOLE FORMATION CAUSED BY THE QCD TRANSITION ?

We consider the evolution of cosmological perturbations at the QCD transition, in particular the sudden reheating from a supercooled universe to the transition temperature. Sudden reheating happens at a specific temperature, hence density, and singles out one specific hypersurface. Underdensities reach the reheating earlier than overdensities, there is a short period of huge pressure differences which leads to a jump in the fluid velocity. Density perturbations of scales far below the Hubble radius λ ≪ R H get an amplification which grows quadratically in wavenumber. Primordial black hole formation will not be sufficiently amplified by the QCD transition unless the initial spectrum is fine tuned. Could primordial black holes of one solar mass be formed because of the QCD transition? Such black holes have been proposed as candidates for massive compact halo objects observed by microlensing. Our analysis leads to the conclusion that the QCD transition cannot provide sufficient amplification on horizon scales to form black holes without fine tuning the initial spectrum. The QCD transition in the early universe took place at a temperature T ⋆ ∼ 150 MeV. Recent results of lattice QCD indicate a first order phase transition 1. The quark-gluon plasma, tightly coupled to photons and leptons, cools via Hubble expansion below T ⋆. At the maximal supercooling 2 , ∆T /T ⋆ ≡ (T ⋆ − T sc)/T ⋆ ≈ 10 −3 , nucleation of hadronic bubbles becomes efficient and the fluid suddenly reheats to the transition temperature, see Fig. 1. Reheating takes only a tiny fraction of the Hubble time 2 , ∆t RH /t H ≈ 10 −6 − 10 −5. The step in temperature implies a step in pressure, ∆p ρ + p = ∆T T ⋆. (1) It is crucial that this leads to large spatial variations of pressure at the time of reheating, since underdense regions get reheated earlier than overdense regions.