Peaks above the Harrison-Zel'dovich spectrum due to the Quark-Gluon to Hadron Transition

We investigate the effect of the quark-gluon to hadron transition at $T_\star\sim 150$ MeV on the evolution of primordial cosmological perturbations, in particular distortions of the Harrison-Zel'dovich spectrum. If the phase transition is first order, the sound velocity vanishes during the transition. Thus, density perturbations fall freely for about a Hubble time. The primordial Harrison-Zel'dovich rms density fluctuations for scales below the Hubble radius at the transition develop peaks and dips, which grow linearly with the wavenumber, both for the hadron-photon-lepton fluid and for cold dark matter. The large peaks in the spectrum may affect primordial black hole formation, big bang nucleosynthesis, and they produce cold dark matter clumps of $10^{-8}$ to $10^{-11} M_\odot$.