Deviations from the Harrison - Zel ’ dovich spectrum due to the Quark - Gluon to Hadron Transition

We investigate the effect of the quark-gluon to hadron transition on the evolution of cosmological perturbations. If the phase transition is first order, the sound speed vanishes during the transition, and density perturbations fall freely. The primordial Harrison-Zel’dovich density fluctuations for scales below the Hubble radius at the transition develop peaks, which grow linearly with the wavenumber, both for the hadron-photon-lepton fluid and for cold dark matter. The large peaks in the spectrum produce cold dark matter clumps of 10 to 10M⊙. QCD makes a transition from a quark-gluon plasma at high temperatures to a hadron gas at low temperatures. Lattice QCD simulations give a transition temperature T⋆ ∼ 150 MeV and indicate a first-order phase transition for the physical values of the u,d,s-quark masses [1]. The relevance of the QCD transition for cosmology, especially for big-bang nucleosynthesis [2], has been discussed before, but the focus was on effects of bubble formation. In this paper and in [3] we look at matter averaged over scales much larger than the bubble separation. We show that for a first order phase transition the sound speed cs = (∂p/∂ρ) 1/2 s drops to zero suddenly at the moment the transition temperature T⋆ is reached, stays zero for the entire time until the phase transition is completed, and afterwards suddenly rises back to cs ≈ c/ √ 3. In contrast the pressure stays positive and varies continuously, although it goes below the radiation fluid value p/ρ = 1/3. Since cs is zero during the transition, there are no pressure perturbations, no pressure gradients, no restoring forces. Pre-existing cosmological perturbations, generated by inflation with a Harrison-Zel’dovich spectrum, go into free fall for about a Hubble time. The superhorizon modes (at the time of the transition) remain unaffected, the subhorizon modes develop peaks in δρ/ρ which grow linearly with Seminar given at Journées Relativistes ’96, Ascona (Switzerland).