Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 192
In Figure 106a we show the case t+ = 10 −4 s and n+ =1.40. In this case we
have important contributions from the QCD transition (βmax ∼ 10 −9 in the case
of a Bag Model, βmax ∼ 10 −14 in the case of a Lattice Fit and βmax ∼ 10 −75
in the case of a Crossover) and an almost negligible contribution from radiation
(βmax ∼ 10 −97 ).
We have also to consider new cases for which the contribution from radiation
is negligible (β < 10 −100 for all tk, cases represented on Table 42 in cyan) but
with some contribution from the QCD phase transition (cf. Table 44 – cases
marked with ‘B’, and Table 45 – cases marked with ‘L’).
In Figure 106b we show the case t+ = 10 −4 s and n+ =1.38, for which we
have only meaningful contributions from the QCD Bag Model (βmax ∼ 10 −13 )
or from the QCD Lattice Fit (βmax ∼ 10 −22 ). In Figure 106c we show the case
t+ = 10 −6 s and n+ =1.30, for which the only relevant contribution comes from
the QCD Bag Model, with βmax ∼ 10 −69 .
In the example of Figure 106d we show the case t+ = 10 −6 s and n+ = 1.40.
Notice that we now have a visible contribution from radiation (βmax ∼ 10 −61 )
as well as an important contribution from the QCD Lattice Fit (βmax ∼ 10 −12 ).
The contribution from the QCD Crossover (βmax ∼ 10 −74 ) is very small, compared
with the others. In this case the QCD Bag Model is excluded, due to
observational constraints.
In Figure 106e we show, as a similar example, the case t+ = 10 −3 s and
n+ =1.44, now with a more important contribution from the QCD Crossover
(βmax ∼ 10 −43 ). The contribution from the Lattice Fit remains important
(βmax ∼ 10 −11 ) and the QCD Bag Model remains excluded. Finally, in Figure
106f we show the case t+ = 10 −2 s and n+ =1.50. In this case we might have
contributions from the QCD Bag Model (βmax ∼ 10 −9 ), from the QCD Lattice
Fit (βmax ∼ 10 −11 ) or from the QCD Crossover (βmax ∼ 10 −28 ).
We might have cases with simultaneous contributions from both QCD and
EW transitions. Those are considered in Section 11.5. We might also have cases
with simultaneous contributions from the QCD phase transition and from the
electron–positron annihilation epoch. We have already presented two examples
of these in Figures 102 and 103.
11.5 EW phase transition (MSSM)
In this section we consider the contribution from the EW phase transition to
the global value of β (in the context of the MSSM and taking into account
the assumptions made at the end of Section 3.2.2). In Table 47 we point out
the cases for which there is a non–negligible contribution from the EW phase
transition.
There are some cases allowed when one considers only the contribution from
radiation but which must be excluded when one takes into account the EW phase
transition. For example, the case t+ = 10 −9 s and n+ =1.36, represented in
Figure 107. This case is not allowed in the context of a first order EW phase
transition. However, if there is no such transition, or if this is not strong enough,