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 198 log 10Βtk log 10Βtk 0 -20 -40 -60 -80 0 -20 -40 -60 -80 a n1.34, log 10t1s7 -10 -8 -6 -4 log10 tk 1 s c n1.40, log 10t1s7 -11 -10 -9 -8 -7 -6 -5 -4 log10 tk 1 s log 10Βtk log 10Βtk 0 -20 -40 -60 -80 0 -20 -40 -60 -80 b n1.36, log 10t1s7 -10 -8 -6 -4 log10 tk 1 s d n1.44, log 10t1s6 -10 -8 -6 -4 log10 tk 1 s Figure 109: The fraction of the universe going into PBHs in a universe with a running–tilt power spectrum when: (a) n+ = 1.34 and t+ = 10 −7 s; (b) n+ = 1.36 and t+ = 10 −7 s (see also Table 48 and Figure 110); (c) n+ =1.40 and t+ = 10 −7 s; (d) n+ =1.44 and t+ = 10 −6 s. The curves represent the contribution from the QCD phase transition (blue – Bag Model; magenta – Lattice Fit; green – Crossover), from the EW phase transition (red), and from radiation (black). Also shown (top of figures, in maroon) are the observational constraints.
PBHs and Cosmological Phase Transitions 199 Table 48: Peaks of the curve β(tk) in the case n+ =1.36 and t+ = 10 −7 s. See Table 40 for the description of different scenarios. Scenario Number Description Figure of peaks 1 2 Radiation + QCD Bag Model 110a 2 2 Radiation + QCD Lattice Fit 110b 3 1 Radiation 110c 4 3 Radiation + EW Bag Model + QCD Bag Model 110d 5 3 Radiation + EW Bag Model + QCD Lattice Fit 110e 6 2 Radiation + EW Bag Model 110f When n+ =1.22 and n+ =1.24 there are a few cases for which the peak from the radiation contribution occurs for tk < 10 −23 s. Taking into account that our expression for β(tk) is classic (Section 5.1), not valid for epochs earlier than ∼ 10 −23 s where the maximum is attained, we consider, for these particular cases, the values correspondent to tk = 10 −23 s (which correspond to PBHs exploding right now), and we show those values in Table 49 inside square brackets. For the QCD Crossover and for the electron–positron annihilation there are a lot of cases for which there is an important contribution to β, similar to the radiation contribution, but without any peak. As an example of this, we mention the case n+ =1.68 and t+ = 100 s (Figure 101f) for which we have a single peak from the radiation contribution. These cases are labeled, in Table 49, with ‘NA’ (meaning Not Applicable).
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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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Page 221 and 222: Table 49 (continued). PBHs and Cosm
Page 223 and 224: Table 49 (continued). Radiation EW
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