Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 127
∆
∆
∆
1.4
1.2
1
0.8
0.6
0.4
0.2
1.4
1.2
0.8
0.6
0.4
0.2
C
B
a
0
0 0.2 0.4 0.6 0.8
∆
b
1 1.2 1.4
1
1.4
1.2
0.8
0.6
0.4
0.2
C
B
A
∆1
0
0 0.2 0.4 0.6 0.8
∆
c
1 1.2 1.4
1
0
C B
A
∆1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆
Figure 51: PBH formation during the QCD transition according to the Bag
Model for the cases: (a) x = 15, (b) x = 30, and (c) x = 90; 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 ≈ 0.29, δBC ≈ 0.18; (b) δAB ≈ 0.20, δBC ≈ 0.13; and (c)
δAB ≈ 0.11, δBC ≈ 0.07. 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 = 15 we have
three intersections points: δc1 ≈ 0.15, δc2 ≈ 0.27 and δc =1/3. This means that
we now have two regions for PBH formation: 0.15 ≤ δ ≤ 0.27 and 1/3 ≤ δ< 1.
In the case x = 30 we have δc1 ≈ 0.12 and δc2 ≈ 0.15 (see text and Figure 50
for more details, adapted from Cardall & Fuller, 1998).
A
∆1