Primordial Black Holes and Cosmological Phase Transitions Report ...

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$Kawasaki dynamic in continuum Math. Encounters XXXV ... - CCM$

Contents List of Figures vii List of Tables xii Acronyms xiv Physical Constants and Parameters xvi Preface xvii 1 The Primordial Universe 1 1.1 Relativistic cosmology . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Universe Timeline . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Cosmological phase transitions . . . . . . . . . . . . . . . . . . . 18 1.5 The Lambda–Cold Dark Matter Model . . . . . . . . . . . . . . . 20 1.6 The scale factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 The Cosmic Microwave Background temperature . . . . . . . . . 28 1.8 The Standard Model of Particle Physics . . . . . . . . . . . . . . 33 1.9 The Minimal Supersymmetric extension of the SMPP . . . . . . 43 1.10 Degrees of freedom . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2 The QCD phase transition 59 2.1 The QCD transition mechanism . . . . . . . . . . . . . . . . . . . 59 2.2 Signatures of the QCD transition . . . . . . . . . . . . . . . . . . 66 2.3 QCD models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.3.1 The Bag Model . . . . . . . . . . . . . . . . . . . . . . . . 69 2.3.2 Lattice Fit . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.3.3 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.4 The duration of the QCD transition . . . . . . . . . . . . . . . . 78 3 The EW phase transition 86 3.1 The critical temperature . . . . . . . . . . . . . . . . . . . . . . . 87 3.2 EW phase transition models . . . . . . . . . . . . . . . . . . . . . 93 3.2.1 Crossover (SMPP) . . . . . . . . . . . . . . . . . . . . . . 93 3.2.2 Bag Model (MSSM) . . . . . . . . . . . . . . . . . . . . . 96 3.3 The baryogenesis problem . . . . . . . . . . . . . . . . . . . . . . 99 4 The electron–positron annihilation 102 5 Fluctuations 106 5.1 The quantum–to–classical transition . . . . . . . . . . . . . . . . 106 5.2 Density fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.3 Fluctuations during the QCD phase transition . . . . . . . . . . 110 5.3.1 Bag Model . . . . . . . . . . . . . . . . . . . . . . . . . . 110 iv
PBHs and Cosmological Phase Transitions v 5.3.2 Lattice Fit . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.3.3 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.4 Fluctuations during the EW phase transition . . . . . . . . . . . 117 5.4.1 Crossover (SMPP) . . . . . . . . . . . . . . . . . . . . . . 117 5.4.2 Bag Model (MSSM) . . . . . . . . . . . . . . . . . . . . . 117 5.5 Fluctuations during the e + e − annihilation . . . . . . . . . . . . . 119 6 PBH formation 120 6.1 The condition for PBH formation . . . . . . . . . . . . . . . . . . 120 6.2 The mechanism of PBH formation . . . . . . . . . . . . . . . . . 121 7 The threshold δc during the QCD epoch 124 7.1 Bag Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.1.1 Before the mixed phase . . . . . . . . . . . . . . . . . . . 124 7.1.2 During the mixed phase . . . . . . . . . . . . . . . . . . . 129 7.1.3 After the mixed phase . . . . . . . . . . . . . . . . . . . . 133 7.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.2 Crossover Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.2.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 7.2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.3 Lattice Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.3.1 Before the mixed phase . . . . . . . . . . . . . . . . . . . 150 7.3.2 During the mixed phase . . . . . . . . . . . . . . . . . . . 152 7.3.3 After the mixed phase . . . . . . . . . . . . . . . . . . . . 152 7.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8 The threshold δc for PBH formation during the EW phase transition 159 8.1 Crossover Model (SMPP) . . . . . . . . . . . . . . . . . . . . . . 159 8.1.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.1.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 8.2 Bag Model (MSSM) . . . . . . . . . . . . . . . . . . . . . . . . . 160 9 The threshold δc for PBH formation during the cosmological e + e − annihilation 167 9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10 Running–tilt power–law spectrum 170 11 The fraction of the Universe going into PBHs 174 11.1 Radiation–dominated universe . . . . . . . . . . . . . . . . . . . . 176 11.2 EW Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 11.3 Electron–positron annihilation . . . . . . . . . . . . . . . . . . . 183 11.4 QCD phase transition . . . . . . . . . . . . . . . . . . . . . . . . 185 11.5 EW phase transition (MSSM) . . . . . . . . . . . . . . . . . . . . 192 11.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
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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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