Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 131
∆
1.4
1.2
1
0.8
0.6
0.4
0.2
x2 x15 x30 x90
∆c2
∆c1 ∆c2
∆c1
No BH formation
BH formation
BH formation
No BH formation
∆c0.7
∆c13
20 40 60 80 100
x
Figure 54: The curve in the (x, δ) plane indicating which parameter values lead
to collapse to a BH, within the QCD Bag Model, in the case x>1 with δc =1/3
and δc =0.7. We show the values of x corresponding to the cases presented in
Figures 50, 51 and 53. The intersection point δc1 = δc2 occurs for x ≈ 54.8 when
δc =1/3 and x ≈ 13.6 when δc =0.7. The intersection point δc2 = δc =1/3
occurs for x ≈ 12.0 when δc =1/3 and x ≈ 3.5 when δc =0.7.
x
50
40
30
20
10
∆c2∆c
∆c1∆c2
0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Figure 55: The value of x as a function of δc for the special cases δc1 = δc2
and δc2 = δc for the QCD phase transition according to the Bag Model. The
dots represent the values obtained numerically (see Table 28) and the solid lines
represent the cubic interpolations (equations 259 and 260).
∆c