We reexamine the recently proposed "little inflation" scenario that allows for a strong first order phase-transition of QCD at non-negligible baryon number in the early universe and its possible observable consequences. The scenario is based on the assumptions of a strong mechanism for baryogenesis and a quasistable QCD-medium state which triggers a short inflationary period of inflation diluting the baryon asymmetry to the value observed today. The cosmological implications are reexamined, namely effects on primordial density fluctuations up to dark matter mass scales of Mmax ∼ 1M ⊙ , change in the spectral slope up to Mmax ∼ 10 6 M ⊙ , production of seeds for the present galactic and extragalactic magnetic fields and a gravitational wave spectrum with a peak frequency around ν peak ∼ 4 · 10 −8 Hz. We discuss the issue of nucleation in more detail and employ a chiral effective model of QCD to study the impact on small scale structure formation.

We explore a scenario that allows for a strong first order phase transition of QCD at a non-negligible baryon number in the early Universe and its possible observable consequences. The main assumption is a quasistable QCD-vacuum state that leads to a short period of inflation, consequently diluting the net baryon to photon ratio to today's observed value. A strong mechanism for baryogenesis is needed to start out with a baryon asymmetry of order unity, e.g., as provided by Affleck-Dine baryogenesis. The cosmological implications are direct effects on primordial density fluctuations up to dark matter mass scales of M{max}∼1-10M{⊙}, change in the spectral slope up to M{max}∼10{6}-10{8}M{⊙}, production of strong primordial magnetic fields and a gravitational wave spectrum with present day peak strain amplitude of up to h{c}(ν{peak})∼5×10{-15} around ν{peak}∼4×10{-8}  Hz.

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We have investigated effects of the QCD phase transition on the relic GW spectrum applying several equations of state for the strongly interacting matter: Besides the bag model, which describes a first order transition, we use recent data from lattice calculations featuring a crossover. Finally, we include a short period of inflation during the transition which allows for a first order phase transition at finite baryon density. Our results show that the QCD transition imprints a step into the spectrum of GWs. Within the first two scenarios, entropy conservation leads to a step-size determined by the relativistic degrees of freedom before and after the transition. The inflation of the third scenario much stronger attenuates the high-frequency modes: An inflationary model being consistent with observation entails suppression of the spectral energy density by a factor of 10 −12 .Theories of inflation predict the existence of a background spectrum of gravitational waves (GWs) which has been created in the very early universe together with scalar perturbations of the energy density. Since then the GWs propagate freely through spacetime still retaining information about the conditions under which they originated. This is because their cross section is very small: Particles with larger cross section, such as neutrinos or photons, decouple much later and therefore carry no information about the universe at such early times and high energies. This advantage of GWs renders their direct detection impossible until today. However, observations of the binary pulsar B1913+16 (Hulse-Taylor pulsar) provide strong evidence for energy loss through emission of gravitational radiation [1].In this article we demonstrate that in spite of being decoupled, relic GWs can show imprints of subsequent cosmic events, e.g. phase transitions. We present the shape of the relic GW spectrum after different scenarios of the QCD phase transition. Before the transition, at about 200 MeV, the universe is filled with a fluid containing relativistic quarks (up, down and strange), gluons, leptons and photons. After the transition, quarks are confined into hadrons of which the pions are the only degrees of freedom which are still relativistic. From this reduction of degrees of freedom and the assumption of entropy conservation, the impact of the phase transition on the spectrum of GWs can be derived. Numerical calculations show that the shape of the spectrum after confinement and chiral symmetry breaking does not strongly depend on the order of the phase transition.However, there are scenarios for the cosmological QCD phase transition where entropy conservation is considerably violated and the gross features of the spectrum are not fixed by the estimates mentioned above. We will discuss a model which includes a short period with dominating vacuum energy density causing inflation. The melting of this energy is associated with a large entropy release. Within this model, the energy density in highfrequency GWs is much more diluted than within the scenarios ...

a b s t r a c tThe QCD phase diagram might exhibit a first order phase transition for large baryochemical potentials. We explore the cosmological implications of such a QCD phase transition in the early universe. We propose that the large baryon-asymmetry is diluted by a little inflation where the universe is trapped in a false vacuum state of QCD. The little inflation is stopped by bubble nucleation which leads to primordial production of the seeds of extragalactic magnetic fields, primordial black holes and gravitational waves. In addition the power spectrum of cold dark matter can be affected up to mass scales of 10 9 M ⊙ . The imprints of the cosmological QCD phase transition on the gravitational wave background can be explored with the future gravitational wave detectors LISA and BBO and with pulsar timing.