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 160 Table 35: The lowest value of δc1,min for the EW Crossover for different values of δc. It is also shown the corresponding values of ∆T/Tc and tk. δc δc1,min ∆T/Tc tk(s) 1/3 0.33186 0.0131 8.32 × 10 −11 0.4 0.39823 0.0091 9.33 × 10 −11 0.5 0.49778 0.0111 1.10 × 10 −10 0.6 0.59734 0.0101 1.23 × 10 −10 0.7 0.69689 0.0101 1.35 × 10 −10 corresponds to the case for which a minimal value for δc1 ≈ 0.33186 is achieved and that occurs for ∆T =0.013Tc. We considered also the cases tk =1.5 × 10 −10 s – Figure 83d (tk t2). For all these cases it is clear that the effect of the EW Crossover, in terms of the reduction of the value of δc, is not as significant as it was for fluctuations crossing the horizon a little bit before the beginning of the transition (cf. Figures 83a and 83b). The value of δc1 smoothly aproaches δc =1/3 as one moves to larger values of tk for all the considered values of ∆T . Figure 84 shows the region on the (log 10(tk/1s), δ) plane for which collapse to a BH occurs in the case of the EW Crossover with δc =1/3 and when ∆T assumes the values 0.001Tc, 0.013Tc and 0.1Tc. Without the phase transition, these would be three straight horizontal lines at δ =1/3. We have also represented, for reference, the location of the EW Crossover. It is clear that the case ∆T =0.013Tc is the most important in the context of PBH production (with δc =1/3). For that reason we will consider, from now on, for the EW Crossover, only this case. Figure 85 indicates the region on the (log 10(tk/1s), δ) plane for which collapse to a BH occurs for δc =1/3 and for δ =0.4. Without the phase transition, these would be two straight horizontal lines at δ =1/3 and δ =0.4. 8.1.2 Summary Due to the EW Crossover the PBH formation threshold δc experiences a reduction on its background value. On Table 36 we present some of these new values δc1 as a function of time for the case δc =1/3. 8.2 Bag Model (MSSM) In the case of an EW first–order phase transition we replace the lower limit in the condition (251) by expression (253). The quantity f, which represents the
PBHs and Cosmological Phase Transitions 161 ∆ ∆ ∆ 0.334 0.3335 0.333 0.3325 0.332 0.3315 0.334 0.3335 0.333 0.3325 0.332 0.3315 0.334 0.3335 0.333 0.3325 0.332 0.3315 tk1 tk2 a tk5 tk4 tk3 0.2 0.4 0.6 0.8 ∆ b 1 1.2 1.4 tk1 tk2 tk5 tk4 tk3 0.2 0.4 0.6 0.8 ∆ c 1 1.2 1.4 tk1 tk2 tk5 tk4 tk3 0.2 0.4 0.6 0.8 1 1.2 1.4 ∆ Figure 82: The curve (1 − f)δc for the EW Crossover when δc = 1/3 and: (a) ∆T = 0.001Tc, (b) ∆T = 0.013Tc and (c) ∆T = 0.1Tc. Different lines correspond to different values of tk: tk1 = 5.0 × 10 −11 s, tk2 = 8.32 × 10 −11 s, tk3 = tEW− =2.3 × 10 −10 s, tk4 =2.7 × 10 −10 s, and tk5 = tEW+ = 3.15 × 10 −10 s.
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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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