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 118 Table 27: Classification of overdense regions according to the state of matter at the horizon crossing and at turnaround for the EW first–order phase transition. x Class Horizon Crossing phase Turnaround phase 2 1.5 1 0.5 A high high B high mixed C high low D mixed mixed E mixed low F low low x1 xy 1 0.460 tEW tEW -9.8 -9.7 -9.6 -9.5 -9.4 Log 10t1s Figure 47: The function x(t) for the EW Bag Model–like phase transition (equation 242).
PBHs and Cosmological Phase Transitions 119 In Figure 47 we show the curve x(t). Equations (219) to (236), derived for the QCD transition, are quite general and, hence, we simply adopt them here without making any changes. Inserting y −1 =0.460 into equation (236) it turns out that δ ≈ 3.4. This result means that class D fluctuations do not exist for δ< 3.7 and that class C fluctuations do not exist for δ> 3.7. 5.5 Fluctuations during the e + e − annihilation We now describe the evolution of a fluctuation during the cosmological electron– positron annihilation process in the same way that we did for the QCD Crossover case (cf. Section 5.3.3). Thus, Rk and Sc are, once again, given by expressions (239) and (240). In addition, the relation between the turnaround instant tc and the horizon crossing time tk will be given by expression (241).
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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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Primordial Black Holes and Cosmological Phase Transitions Report ...

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