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 58 Figure 12: The effective number of degrees of freedom g(T ). The full line is the prediction of the SMPP, the dashed line shows the MSSM, according to the SPS1a scenario (see Section 1.9). Below T ∼ 1 MeV we have to consider, separately, the effective number of degrees of freedom of the energy density here represented by gε, and the number of degrees of freedom of the entropy density, gs (adapted from Schwarz, 2003).
PBHs and Cosmological Phase Transitions 59 2 The QCD phase transition 2.1 The QCD transition mechanism When the age of the Universe was ∼ 10 −5 s a spontaneous breaking of the chiral symmetry 25 of QCD occured. As a result, quarks and gluons became confined in hadrons. In recent years most attention has focussed on the possibility of recreating the Quark–Gluon Plasma (QGP) in terrestrial laboratories in relativistic heavy– ion collisions. Extensive experimental work is currently being done with heavy ion collisions to study the QCD transition (most recently at the Relativistic Heavy Ion Collider, RHIC) (e.g. Aoki et al., 2006b). At the QCD epoch the Universe can be treated as a radiation fluid made up of quarks, gluons, leptons and photons (e.g. Boyanovsky et al., 2006). Baryons are tightly coupled to the radiation fluid at the QCD scale. Their energy density is negligible with respect to that of the other relativistic particles and their chemical potential is negligible µB ≈ 0 (e.g. Schwarz, 2003). Both for the cosmological transition and for RHIC, the net baryon densities are quite small, and so the baryonic chemical potential is much less than the typical hadron masses (≈ 45 MeV at RHIC and negligible in the early Universe). A calculation at µ = 0 is directly applicable for the cosmological transition and most probably also determines the nature of the transition at the RHIC (e.g. Aoki et al., 2006a,b). There is some apparent similarity in cosmology and heavy–ion collision physics. From present observations of remote objects in the Universe, we look into the past. Combining observational facts, like the distribution and the redshift of galaxies, one can develop a picture of the early stages of the Universe. The situation in heavy–ion collision physics is very similar to this one. Observing the created hadrons at a very late stage, one tries to extrapolate back to the hottest and densest stages. Due to this similarity the process of heavy–ion collision is sometimes called the Little Bang. Notice, however, that we are dealing with different scales in both cases and that in the case of the Big Bang we are also dealing with an expanding Universe (e.g. Kämpfer, 2000). In recent years, considerable efforts have been devoted to the determination of the phase diagram of QCD at finite temperature and density. In Figure 13 we have a schematic representation of the QCD phase transition for different choices of the quark masses mu,d and ms when µ = 0. In the limits of zero and infinite quark masses (lower left and upper right corners), order parameters corresponding to the breaking of a symmetry can be defined, and one finds, numerically, that a first–order transition takes place at a finite temperature Tc. On the other hand, one observes an analytic crossover at intermediate quark masses. Hence, each corner must be surrounded by a region of first– 25 Chiral symmetry is a symmetry of QCD in the limit of vanishing quark masses. We know, however, that quark masses are finite (see Table 5). But compared with hadronic scales the masses of the two lightest quarks, up and down, are very small, so that chiral symmetry may be considered an approximate symmetry of the strong interactions (e.g. Koch, 1997).
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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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