Primordial Black Holes and Cosmological Phase Transitions Report ...

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$Kawasaki dynamic in continuum Math. Encounters XXXV ... - CCM$

PBHs and Cosmological Phase Transitions 66 transformation (see Schmid et al., 1999, for more details). The expansion of the Universe is very slow compared to the strong, electromagnetic and weak interactions around Tc. Thus, leptons, photons and the QGP/HG are in thermal and chemical equilibrium at cosmological time scales. All components have the same temperature locally, i.e., smeared over scales of ∼ 10 −7 RH. At larger scales, strongly, weakly and electromagnetically interacting matter makes up a single perfect (i.e. dissipationless) radiation fluid (e.g. Schmid et al., 1999). In the case of a Crossover, instead of a first–order phase transition, the sound speed decreases but does not vanish completely (e.g. Kämpfer, 2000). If the Crossover is smooth, then no out–of–equilibrium aspects are expected as the system will evolve in LTE (e.g. Boyanovsky et al., 2006). If there is some cosmic dirt in the Universe such as PBHs, monopoles, strings, and other kinds of defects, then the typical nucleation distance may differ significantly from the scenario of homogeneous nucleation. That is because, in a first–order phase transition, the presence of impurities lowers the energy barrier and, thereby, the maximum amount of superccoling achieved during the transition (Christiansen & Madsen, 1996). A sketch of inhomogeneous bubble nucleation is shown in Figure 19. The basic idea is that temperature inhomogeneities determine the location of bubble nucleation. In cold regions, bubbles nucleate first. However, if the mean distance between bubbles (∆nuc) is larger than the amplitude of the fluctuations δrms, then the temperature inhomogeneities are negligible and the phase transition proceeds via homogeneous nucleation (Boyanovsky et al., 2006). 2.2 Signatures of the QCD transition A strong first–order QCD phase transition could lead to observable signatures today. That is because, during phase coexistence, the Universe is effectively unstable to gravitational collapse for all scales exceeding the mean distance between hadron or quark–hadron bubbles (e.g. Jedamzik, 1998). There are two kinds of effects emerging from the cosmological QCD phase transition: the ones that affect scales λ ≤ dnuc (e.g. formation of quark nuggets, generation of isothermal baryon fluctuations, generation of magnetic fields and gravitational waves) and the ones that affect scales λ ≤ RH (e.g. formation of CDM clumps, modification of primordial gravitational waves, formation of PBHs). As the first–order phase transition weakens, these effects become less pronounced. Recent results provide strong evidence that the QCD transition is a Crossover (cf. Section 2.3.3) and thus the above scenarios (and many others), which arise from a strong first–order phase transition, are ruled out (e.g. Aoki et al., 2006b). Bearing this in mind, we briefly describe some of the mentioned QCD signatures.
PBHs and Cosmological Phase Transitions 67 Figure 19: Sketch of a first–order QCD transition in the inhomogeneous Universe: at t1 the coldest spots (dark gray) are cold enough to render the nucleation of hadronic bubbles (H) possible, while most of the Universe remains in the quark–gluon phase (Q). At t2 >t1 the bubbles from the cold spots have merged and have grown to bubbles as large as the fluctuation scale. Only the hot spots (light gray) are still in the QGP phase. At t3 the transition is almost finished. The last QGP drops are found in the hottest spots of the Universe. The mean separation of these hot spots can be much larger than the homogeneous bubble nucleation separation (Ignatius & Schwarz, 2001). Quark nuggets Bodmer (1971) suggested the possibility that strange quark matter might be the ground state of bulk matter, instead of 56 Fe. The idea of strange quark matter is based on the observation that the Pauli Principle allows more quarks to be packed into a fixed volume in phase space if three instead of two flavours are available. Thus, the energy per baryon would be lower in strange quark matter than in nuclei. However, the strange quark is heavy compared with the up and down quarks, which counteracts the advantage from the Pauli Principle (e.g. Boyanovsky et al., 2006). Witten (1984) pointed out that a separation of phases during the coexistence of the hadronic and the quark phase could gather a large number of baryons in strange quark nuggets. These quark nuggets could contribute to the dark matter existing today (e.g. Boyanovsky et al., 2006). However, it was realized that the quark nuggets would evaporate when the temperature is above 50 MeV (e.g. Boyanovsky et al., 2006). While cooling, the quark nuggets lose baryons unless they contain much more than 10 44 baryons initially. The number of baryons inside an Hubble volume at the QCD epoch is ∼ 10 50 which implies that dnuc should have been of ∼ 300 m in order to allow quark nugget formation. This is ∼ 10 4 too large compared to the dnuc suggested by recent lattice results (e.g. Schmid et al., 1999).
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CCM-Centro de Ciências Matemática
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Contents List of Figures vii List o
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PBHs and Cosmological Phase Transit
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List of Tables 1 The Universe timel
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Table 49 (continued). PBHs and Cosm
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Table 49 (continued). Radiation EW
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