Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 148
∆
0.8
0.7
0.6
0.5
0.4
0.3
BH formation
∆c1 ∆c0.7
BH formation
∆c1 ∆c13
t1
No BH formation
-5 -4.5 -4 -3.5 -3
Log10tk1s Figure 70: The curve in the (log 10 (tk/1s),δ) plane indicating which parameter
values lead to collapse to a BH in the case of a QCD Crossover with δc =1/3
and with δc =0.7. We have also represented, for reference, the values of t1 and
t2 giving the locus of the transition (note that, in both cases, the BH formation
region extends up to δ = 1).
as it does for the Bag Model. In fact, there is a period (t1 ≤ t ≤ t−) during
which the sound speed value drops from 1/ √ 3 to zero (cf. Figure 30).
We need to write a function f suitable to the Lattice Fit. For the period
t1 ≤ t ≤ t− we adopt the ideas from the Crossover case (Section 7.2); for the
period t− ≤ t ≤ t+ we consider the Bag Model results (Section 7.1).
Let us start with fluctuations of class A. We have fA = 0, as in the Bag
Model case, only if tc