Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 213
12.1.2 EW phase transition
The EW phase transition (Section 3) was responsible for the spontaneous EW
symmetry breaking which gave mass to all massive particles. Within the context
of the SMPP, the EW phase transition is a very smooth Crossover (Section 3.2.1)
with ∆g ∼ 1.
Taking this into account, we tried to determine which value of the parameter
∆T (see equation 180) would give rise to the strongest effect in terms of the
reduction of δc (Section 8.1). We found out that, in the case δc =1/3, we should
have ∆T ≈ 0.013Tc in order to get δc,min ≈ 0.332 which reflects, in practical
terms, an almost negligible variation (Figure 85).
As a result we found out that the EW Crossover has no visible effects in
terms of PBH production (Section 11.2). This means that when working in the
context of the SMPP, one can safely neglect the EW transition as a potential
source of PBH production.
A first–order phase transition might be allowed for the EW but only in the
context of some extensions of the SMPP, such as the speculative framework of
the MSSM (Section 1.9). We have considered that possibility and modelled it
by a Bag Model (Section 3.2.2) with ∆g ≈ 80 (which appears to be a reasonable
value in the context of the MSSM). In this case the results are, by far, more
interesting (Section 8.2) than in the Crossover case. We obtained a reduction
from δc =1/3 to δc,min ≈ 0.17 (Figure 86).
In Section 11.5 we determined the contribution from the EW Bag Model to
the curve β(tk). Some of the results are encouraging, with the curve showing
two peaks. For example, in the case shown in Figure 108c we have a large
peak representing the radiation contribution and a sharp peak representing the
contribution from the EW phase transition.
There are a few cases for which the contribution from the EW exceeds the
observational constraints (cf. Table 47). These must be excluded. On the other
hand, there are also a few extra cases (i.e. cases not shown on Table 42) for
which, although the contribution from radiation is negligible, there is a non–
negligible contribution from the EW transition (e.g. Figure 108a).
We also have cases for which there is a significant contribution from both
the QCD and the EW transitions. An example of this is the case shown in
Figure 109a for which we have two sharp peaks. Notice, however, that the
peak on the right, which relates to the QCD, exists only in the case of the Bag
Model or the Lattice Fit model. In the example of Figure 109b we have, besides
the contribution from the EW phase transition, a (modest) contribution from
radiation and a possible contribution from the QCD phase transition (valid only
if one adopts the Bag Model or the Lattice Fit).
Cut from Table 49, in Table 53 we present a list with the ten largest contributions
from the EW Bag Model. In each case we have also indicated the
contribution from radiation.