Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 155
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Figure 78: PBH formation during the QCD transition according to the Lattice
Fit, when δc =1/3, for the cases: (a) x =0.70 (tk ≈ 1.2 × 10 −4 s); (b) x =0.47
(tk ≈ 1.5 × 10 −4 s). The solid curve corresponds to the function (1 − f)δc and
the dashed curve corresponds to the identity δ. The new threshold for PBH
formation is: (a) δc1 ≈ 0.32; (b) δc1 ≈ 0.33. The borders between classes C, E,
and F are given by: (a) δCE ≈ 0.44, δEF ≈ 0.045; (b) δCE ≈ 1.12, δEF ≈ 0.54.
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Figure 79: PBH formation during the QCD transition according to the Lattice
Fit for the cases: (a) x =0.70 and (b) x =0.47. 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. For the borders between the different classes of fluctuations see Figure 78.
x =0.70 (tk ≈ 1.2 × 10 −4 s) when δc =1/3. PBHs could form , in this case,
from fluctuations of classes C and E. Fluctuations of class F dissipate without
forming a PBH. Fluctuations of class E also dissipate when δ< 0.322. This
point δc1 ≈ 0.322 marks the new threshold for PBH formation during the QCD
phase transition when x =0.70.
As a second example we show in Figure 78b the plot for the case x ≈ 0.47
(tk ≈ 1.5 × 10 −4 s), when δc =1/3. In this case PBHs could form from fluctuations
of class E and F but no longer from fluctuations of class C. The new
threshold for PBH formation is now δc1 ≈ 0.326.
In Figure 79 we consider, once again, the cases x =0.70 and x =0.47 but
now with δc assuming several values between 1/3 and 0.7.
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