Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 195
log 10Βtk
0
-20
-40
-60
-80
n1.36, log 10t1s9
-14 -12 -10 -8 -6 -4
log10 tk
1 s
Figure 107: The fraction of the universe going into PBHs in a universe with
a running–tilt power spectrum when n+ =1.36 and t+ = 10 −9 s. The curves
represent the contribution from the EW phase transition (red), from the QCD
phase transition (blue, Bag Model) and from radiation (black). The maroon
line represents the observational constraints, which are violated here by the
EW phase transition contribution.
then this case becomes valid, with a possible contribution also from the QCD
transition (Bag Model).
There are a few cases for which the contribution from radiation is negligible
(i.e., cases shown in cyan on Table 42) but with an appreciable contribution
from the EW phase transition. These cases are labeled on Table 47 with ‘E’,
‘BE’ and ‘BLE’. In Figures 108a and 108b we present, as examples, the cases
t+ = 10 −10 s and n+ =1.28, and t+ = 10 −9 s and n+ =1.32, with, respectively,
βmax ∼ 10 −60 and βmax ∼ 10 −23 .
There are also a lot of cases for which we have a contribution from the
EW phase transition as well as from radiation (cf. Table 47, labeled ‘RE’). In
Figures 108c and 108d, we show as examples of this, the cases t+ = 10 −13 s
and n+ =1.32, and t+ = 10 −12 s and n+ =1.34. Notice that in both cases the
two contributions are quite comparable (in terms of βmax). In the first case we
have βmax ∼ 10 −24 from radiation and βmax ∼ 10 −28 from the EW transition,
and in the second case we have βmax ∼ 10 −18 from radiation and βmax ∼ 10 −12
from the EW transition.
In Figures 108e and 108f we present two mores cases with contributions
from radiation and from the EW phase transition. Notice that in these cases
the contribution from the EW phase transition is a lot more relevant than
the contribution from radiation. For example, in the case t+ = 10 −10 s and
n+ = 1.32, represented in Figure 108f, we have that the contribution from
radiation gives βmax ∼ 10 −71 and the contribution from the EW transition