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 200 log 10Βtk log 10Βtk log 10Βtk 0 -20 -40 -60 -80 0 -20 -40 -60 -80 0 -20 -40 -60 -80 a Scenario 1 -10 -8 -6 -4 log10 tk 1 s c Scenario 3 -10 -8 -6 -4 log10 tk 1 s e Scenario 5 -10 -8 -6 -4 log10 tk 1 s log 10Βtk log 10Βtk log 10Βtk 0 -20 -40 -60 -80 0 -20 -40 -60 -80 0 -20 -40 -60 -80 b Scenario 2 -10 -8 -6 -4 log10 tk 1 s d Scenario 4 -10 -8 -6 -4 log10 tk 1 s f Scenario 6 -10 -8 -6 -4 log10 tk 1 s Figure 110: The fraction of the universe going into PBHs in a universe with a running–tilt power spectrum when n+ = 1.36 and t+ = 10 −7 s (see also Figure 109b and Table 48). The curves represent the contribution from the QCD phase transition (blue – Bag Model; magenta – Lattice Fit), from the EW phase transition (red – Bag Model), and from radiation (black). Also shown (top of figures, in maroon) are the observational constraints. Each Figure represents a different scenario (see Table 40 for the description of different scenarios): (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; (d) Scenario 4; (e) Scenario 5; (f) Scenario 6. The contribution from the QCD Crossover (scenarios 3 and 6) is not shown because it is negligible. The contribution from the electron–positron annihilation is also negligible. Assembling these six Figures in a single one we recover Figure 109b.
PBHs and Cosmological Phase Transitions 201 Table 49: The fraction of the universe going into PBHs during radiation domination and during cosmological phase transitions. The value t+ corresponds to the instant for which the value of the spectral index attains its maximum n+. The value tk,max corresponds to the instant for which β attains its maximum value (βmax). A gray background means that the value of βmax exceeds the observational constraints. A coloured background means that the value of βmax belongs to the top ten highest contributions for a particular transition model: EW Bag Model (red, Table 53), QCD Bag Model (blue, Table 51), QCD Lattice Fit (magenta, Table 52), QCD Crossover (green, Table 50), and electron–positron annihilation (cyan, Table 54). We have labeled with ‘NA’ (not applicable) situations for which the curve of β(tk) exists but does not show any maximum, with ‘A’ the cases for which the radiation peak is always hidden (column 4), and with ‘S’ the cases for which the radiation peak is only sometimes hidden (column 4). Values inside square brackets correspond to situations for which the peak from radiation occurs for tk < 10−23 s (see text for more details). Radiation EW Bag Model QCD Bag Model QCD Lattice Fit QCD Crossover e − e + Crossover log10( t+ 1s ) log10( tk,max 1s ) log10 βmax log10( tk,max 1s ) log10 βmax log10( tk,max 1s ) log10 βmax log10( tk,max 1s ) log10 βmax log10( tk,max 1s ) log10 βmax log10( tk,max 1s ) log10 βmax n+ 1.22 -23 [-23] [-74] – – – – – – – – – – -22 [-23] [-79] – – – – – – – – – – -21 -22.6 -98 – – – – – – – – – – 1.24 -23 [-23] [-31] – – – – – – – – – – -22 [-23] [-33] – – – – – – – – – – -21 -22.7 -41 – – – – – – – – – – -20 -21.7 -54 – – – – – – – – – – -19 -20.7 -71 – – – – – – – – – – -18 -19.6 -94 – – – – – – – – – – 1.26 -19 -20.7 -31 – – – – – – – – – – -18 -19.7 -42 – – – – – – – – – – -17 -18.7 -56 – – – – – – – – – – -16 -17.6 -76 – – – – – – – – – – 1.28 -18 -19.8 -19 – – – – – – – – – – -17 -18.7 -26 – – – – – – – – – – -16 -17.7 -36 – – – – – – – – – – -15 -16.7 -49 – – – – – – – – – – -14 -15.6 -68 – – – – – – – – – – -13 -14.6 -94 -10.6 -90 – – – – – – – – -12 – – -10.6 -69 – – – – – – – – -11 – – -10.6 -60 – – – – – – – – -10 – – -10.6 -60 – – – – – – – – -9 – – -10.6 -75 – – – – – – – – (continues on next page)
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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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