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 156 ∆ 1.2 1 0.8 0.6 0.4 0.2 No BH formation BH formation ∆cA No BH formation ∆c2 ∆c1 t t -9 -8 -7 -6 -5 -4 -3 Log 10tk1s Figure 80: The curve in the (log 10(tk/1s), δ) plane indicating which parameter values lead to collapse to a BH in the case of the QCD Lattice Fit when δc =1/3. The vertical dashed lines correspond to tk = t− and tk = t+. 7.3.4 Summary We now compile the results obtained on sections 7.3.1–7.3.3. We have determined the threshold δc for the entire QCD phase transition according to the Lattice Fit model. As a result we obtain Figure 80 for the case δc =1/3 and Figure 81 for the case δc =0.7. During the QCD transition, the threshold for PBH formation (δc) experiences a reduction. As a result, a new window for PBH formation (between δc1 and δc, between δcA and δc or between δc1 and δc2) is opened for a brief period. Note that the window between δcA and δc does not exist for the Bag Model case (Section 7.1.4) because, in that case, we have fA = 0. On Table 34 we present some values for this new threshold for PBH formation during the QCD transition according to the Lattice Fit, when δc =1/3.
PBHs and Cosmological Phase Transitions 157 Table 34: The evolution of δcA, δc1 and δc2 (where applicable) as a function of time for a QCD phase transition according to the Lattice Fit Model when δc =1/3. log 10 (tk/1 s) δcA δc2 δc1 -7.5 0.3304 – – -7.4 0.3301 – – -7.3 0.3297 – – -7.2 0.3292 – – -7.1 0.3287 – – -7.0 0.3281 – – -6.9 0.3274 – – -6.8 0.3267 – – -6.7 0.3258 – – -6.6 0.3249 – – -6.5 0.3238 – – -6.4 0.3226 – – -6.3 0.3212 – – -6.2 0.3196 – – -6.1 0.3178 – – -6.0 0.3157 – – -5.9 0.3133 – – -5.8 0.3105 – – -5.7 0.3073 – – -5.6 0.3036 – – -5.5 0.2992 – – -5.4 0.2940 – – -5.3 0.2877 – – -5.2 0.2800 – – -5.1 0.2702 – – -5.0 0.2573 0.1450 0.1334 -4.9 0.2381 0.1941 0.1554 -4.8 – – 0.1784 -4.7 – – 0.2016 -4.6 – – 0.2242 -4.5 – – 0.2453 -4.4 – – 0.2644 -4.3 – – 0.2813 -4.2 – – 0.2960 -4.1 – – 0.3090 -4.0 – – 0.3182 -3.9 – – 0.3236
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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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