Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 178
log 10Βtk
0
-10
-20
-30
-40
-20 -15 -10 -5 0 5 10
log10 tk
1 s
Figure 93: Observational constraints on β(tk). The vertical dashed line
(tk = 10 5 s) corresponds to an horizon mass of ∼ 10 10 M⊙ (adapted from
Carr, 2005).
10 −16 s ≤ t+ ≤ 10 −11 s which is suitable for PBH formation. Cases with
t+ < 10 −16 s are not allowed and cases with t+ > 10 −11 s are allowed but with
negligible results.
We studied the intervals of this permitted window for different values of n+
(between 1.20 and 2.00). The window moves to later epochs as one moves to
larger values of n+. As a lower limit, for n 10 10 M⊙).
11.2 EW Crossover
It was already mentioned that, in the context of the SMPP, the EW transition
is a very smooth Crossover (Section 3.2.1). As a consequence of this, the contribution
from the EW Crossover to the value of β(tk) is very small. In fact, in
this case, the new threshold δc1 stays always very close to δc (see Table 36).
We consider, as an example, t+ = 10 −8 s and n+ =1.40. In this case, the
contribution from the EW Crossover to the total value of β(tk) is negligible (of
order unity – Figure 100) 34 . On the face of this, we neglect all contributions
34 In order to properly read this graphic start on the left and move across the black line