Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 156
∆
1.2
1
0.8
0.6
0.4
0.2
No BH formation
BH formation
∆cA
No BH formation
∆c2
∆c1
t t
-9 -8 -7 -6 -5 -4 -3
Log 10tk1s
Figure 80: The curve in the (log 10(tk/1s), δ) plane indicating which parameter
values lead to collapse to a BH in the case of the QCD Lattice Fit when δc =1/3.
The vertical dashed lines correspond to tk = t− and tk = t+.
7.3.4 Summary
We now compile the results obtained on sections 7.3.1–7.3.3. We have determined
the threshold δc for the entire QCD phase transition according to the
Lattice Fit model. As a result we obtain Figure 80 for the case δc =1/3 and
Figure 81 for the case δc =0.7.
During the QCD transition, the threshold for PBH formation (δc) experiences
a reduction. As a result, a new window for PBH formation (between δc1
and δc, between δcA and δc or between δc1 and δc2) is opened for a brief period.
Note that the window between δcA and δc does not exist for the Bag Model
case (Section 7.1.4) because, in that case, we have fA = 0. On Table 34 we
present some values for this new threshold for PBH formation during the QCD
transition according to the Lattice Fit, when δc =1/3.