Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 153
∆
1.4
1.2
1
0.8
0.6
0.4
0.2
0
C
B
A
a
∆1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆
∆
1.4
1.2
1
0.8
0.6
0.4
0.2
0
C B
A
b
∆1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆
Figure 74: PBH formation during the QCD transition according to the Lattice
Fit for the cases: (a) x = 25, and (b) x = 50; with δc = 1/3. The solid
curve corresponds to the function (1 − f)δc and the dashed curve corresponds
to the identity δ. The borders between the different classes are given by: (a)
δAB ≈ 0.19, δBC ≈ 0.16; (b) δAB ≈ 0.20, δBC ≈ 0.13. Collapse to a BH occurs
for values of δ for which the dashed line is above the solid curve (while δ< 1).
In the case x = 25 we have three intersections points: δc1 ≈ 0.15, δc2 ≈ 0.17
and δc =0.25. This means that, in this case, there are two regions for PBH
formation: 0.15 ≤ δ ≤ 0.17 and 0.25 ≤ δ< 1. In the case x = 50 PBHs form if
0.27 ≤ δ< 1.
∆
∆
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1.4
1.2
1
0.8
0.6
0.4
0.2
0
C
a
∆1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆
C
B
A
c
∆1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆
A
∆
∆
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1.4
1.2
1
0.8
0.6
0.4
0.2
0
C
B
b
A
∆1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆
C B
A
d
∆1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆
Figure 75: PBH formation during the QCD transition according to the Lattice
Fit for the cases: (a) x = 2, (b) x = 15, (c) x = 25, and (d) x = 50. The solid
curve corresponds to the function (1 − f)δc with, from bottom to top, δc =1/3,
δc =0.4, δc =0.5, δc =0.6 and δc =0.7. In red we show the region where
PBH formation takes place. The borders between the different classes (which
do not depend on the value of δc) are given by: (a) δAC =0.95; (b) δAB ≈ 0.25,
δBC ≈ 0.21; (c) δAB ≈ 0.19, δBC ≈ 0.16; and (d) δAB ≈ 0.14, δBC ≈ 0.10.