Primordial Black Holes and Cosmological Phase Transitions Report ...
Primordial Black Holes and Cosmological Phase Transitions Report ... Primordial Black Holes and Cosmological Phase Transitions Report ...
PBHs and Cosmological Phase Transitions x 73 Regions in the (δk, log 10 x) plane corresponding to the different classes of perturbations for the QCD Lattice Fit. . . . . . . . . . 152 74 PBH formation during the QCD transition according to the Lattice Fit for the cases x = 25 and x = 50 when δc =1/3. . . . . . 153 75 PBH formation during the QCD transition according to the Lattice Fit for the cases x = 2, x = 15, x = 25, and x = 50 when δc assumes different values. . . . . . . . . . . . . . . . . . . . . . . . 153 76 PBH formation during the QCD transition, according to the Lattice Fit, for the cases x =0.985 and x =0.871 when δc =1/3. . . 154 77 The same as Figure 76 but now with the threshold δc assuming different values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 78 PBH formation during the QCD transition according to the Lattice Fit for the cases x =0.70 and x =0.47 when δc =1/3. . . . 155 79 The same as Figure 78 but now with the threshold δc assuming different values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 80 The curve in the (log 10 (tk/1s), δ) plane indicating which values lead to collapse to a BH in the case of the QCD Lattice Fit when δc =1/3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 81 The curve in the (log 10 (tk/1s), δ) plane indicating which values lead to collapse to a BH in the case of the QCD Lattice Fit when δc =0.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 82 The curve (1 − f)δc for the EW Crossover when δc =1/3 with ∆T assuming different values. . . . . . . . . . . . . . . . . . . . . 161 83 PBH formation during the EW Crossover when δc =1/3. . . . . 162 84 The curve in the (log 10(tk/1s), δ) plane indicating which values lead to the formation of a BH, during the EW Crossover, when δc =1/3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 85 The curve in the (log 10(tk/1s), δ) plane indicating which values lead to collapse to a BH during the EW Crossover when δc =1/3 and when δc =0.7. . . . . . . . . . . . . . . . . . . . . . . . . . . 163 86 The curve indicating which values lead to collapse to a BH when δc =1/3 during the EW transition within the MSSM. . . . . . . 165 87 The curve in the (log 10(t/1s),δ) plane indicating which values lead to collapse to a BH when δc =0.7 during the EW transition within the MSSM. . . . . . . . . . . . . . . . . . . . . . . . . . . 166 88 PBH formation during the cosmological electron–positron annihilation when δc =1/3. . . . . . . . . . . . . . . . . . . . . . . . 168 89 The curve on the (log 10 tk, δ) plane indicating which values lead to collapse to a BH during the cosmological electron–positron annihilation when δc =1/3. . . . . . . . . . . . . . . . . . . . . . 168 90 The curve on the (log 10 tk, δ) plane indicating which values lead to collapse to a BH in the case of the cosmological electron– positron annihilation when δc =1/3 and when δc =0.7. . . . . . 169 91 The curves n2(t+) and n3(t+) for different values of nmax. . . . . 172 92 The region on the (n2, n3) plane that leads to a blue spectrum. . 172 93 Observational constraints on β(tk) . . . . . . . . . . . . . . . . . 178
PBHs and Cosmological Phase Transitions xi 94 β(tk) for a radiation–dominated universe when n+ =1.30 and t+ = 10 −17 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 95 β(tk) for a radiation–dominated universe when n+ =1.30 and 10 −17 s ≤ t+ ≤ 10 −11 s . . . . . . . . . . . . . . . . . . . . . . . . 179 96 β(tk) for a radiation–dominated universe when n+ =1.30 and t+ = 10 −10 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 97 β(tk) for a radiation–dominated universe when n+ =1.84 and t+ = 10 4 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 98 β(tk) for a radiation–dominated universe when n+ =1.88 and t+ = 10 5 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 99 β(tk) for a radiation–dominated universe when n+ =2.00 and t+ = 10 7 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 100 The fraction of the universe going into PBHs during the EW Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 101 The fraction of the universe going into PBHs during the electron– positron annihilation epoch (examples). . . . . . . . . . . . . . . 186 102 β(tk) when n+ =1.56 and t+ = 10 −1 s . . . . . . . . . . . . . . . 187 103 β(tk) when n+ =1.54 and t+ = 10 −2 s . . . . . . . . . . . . . . . 187 104 β(tk) when n+ =1.48 and t+ = 10 −4 s . . . . . . . . . . . . . . . 191 105 β(tk) when n+ =1.52 and t+ = 10 −3 s . . . . . . . . . . . . . . . 191 106 The fraction of the universe going into PBHs during the QCD phase transition (examples) . . . . . . . . . . . . . . . . . . . . . 193 107 β(tk) when n+ =1.36 and t+ = 10 −9 s . . . . . . . . . . . . . . . 195 108 The fraction of the universe going into PBHs during the EW phase transition (examples) . . . . . . . . . . . . . . . . . . . . . 197 109 The fraction of the universe going into PBHs with simultaneous contributions from the EW and QCD phase transitions . . . . . . 198 110 The fraction of the universe going into PBHs with simultaneous contributions from the EW and QCD phase transitions . . . . . . 200
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PBHs <strong>and</strong> <strong>Cosmological</strong> <strong>Phase</strong> <strong>Transitions</strong> xi<br />
94 β(tk) for a radiation–dominated universe when n+ =1.30 <strong>and</strong><br />
t+ = 10 −17 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179<br />
95 β(tk) for a radiation–dominated universe when n+ =1.30 <strong>and</strong><br />
10 −17 s ≤ t+ ≤ 10 −11 s . . . . . . . . . . . . . . . . . . . . . . . . 179<br />
96 β(tk) for a radiation–dominated universe when n+ =1.30 <strong>and</strong><br />
t+ = 10 −10 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180<br />
97 β(tk) for a radiation–dominated universe when n+ =1.84 <strong>and</strong><br />
t+ = 10 4 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180<br />
98 β(tk) for a radiation–dominated universe when n+ =1.88 <strong>and</strong><br />
t+ = 10 5 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182<br />
99 β(tk) for a radiation–dominated universe when n+ =2.00 <strong>and</strong><br />
t+ = 10 7 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182<br />
100 The fraction of the universe going into PBHs during the EW<br />
Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183<br />
101 The fraction of the universe going into PBHs during the electron–<br />
positron annihilation epoch (examples). . . . . . . . . . . . . . . 186<br />
102 β(tk) when n+ =1.56 <strong>and</strong> t+ = 10 −1 s . . . . . . . . . . . . . . . 187<br />
103 β(tk) when n+ =1.54 <strong>and</strong> t+ = 10 −2 s . . . . . . . . . . . . . . . 187<br />
104 β(tk) when n+ =1.48 <strong>and</strong> t+ = 10 −4 s . . . . . . . . . . . . . . . 191<br />
105 β(tk) when n+ =1.52 <strong>and</strong> t+ = 10 −3 s . . . . . . . . . . . . . . . 191<br />
106 The fraction of the universe going into PBHs during the QCD<br />
phase transition (examples) . . . . . . . . . . . . . . . . . . . . . 193<br />
107 β(tk) when n+ =1.36 <strong>and</strong> t+ = 10 −9 s . . . . . . . . . . . . . . . 195<br />
108 The fraction of the universe going into PBHs during the EW<br />
phase transition (examples) . . . . . . . . . . . . . . . . . . . . . 197<br />
109 The fraction of the universe going into PBHs with simultaneous<br />
contributions from the EW <strong>and</strong> QCD phase transitions . . . . . . 198<br />
110 The fraction of the universe going into PBHs with simultaneous<br />
contributions from the EW <strong>and</strong> QCD phase transitions . . . . . . 200
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