Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 99
cs 2
0.4
0.3
0.2
0.1
0
tEW
tEW
-9.7 -9.6 -9.5 -9.4 -9.3
Log 10t1s
Figure 41: The sound speed c2 s (t) for the EW phase transition according to the
Bag Model with Tc = 100 GeV. During the coexistence phase, which occurs
between the instants tEW− = 2.3 × 10−10 s (see text for more details) and
tEW+ =3.15 × 10−10 s, the sound speed drops to zero.
Considering Tc = 100 GeV we obtain, with the help of equation (186), the value
tEW+ = 3.15 × 10 −10 s. In order to determine the value of tEW− one must
determine first the value of ∆R. This is a problem, because we need to know the
value of ∆g = gh −gl (see equation 187). We consider, for gl (i.e., the number of
degrees of freedom at the end of the transition), in accordance with the SMPP,
the value gl = 95.25. However, we do not have any clue for the real value of
gh. In the context of the MSSM it may be as large as 228.75 when all particles
and superpartners are present (cf. Table 15) and, in the context of the SMPP
it is gh = 96.25. Within this range of values ∆R varies between ≈ 1.0035 and
≈ 1.3392. Inserting this values into equation (189) with tEW+ =3.15 × 10 −10 s
it turns out that tEW− should be between 2.03 × 10 −10 s and 3.13 × 10 −10 s.
We consider here tEW− =2.3 × 10 −10 s, corresponding to ∆g ≈ 80. In
Figure 41 we show the sound speed profile for the EW transition, according to
these results. It must be noted, however, that the value of tEW− was introduced
only with the purpose of giving an example. At this stage, we do not have any
observational evidence supporting this or any other value. In fact, we do not
have any concludent results on the existence of extensions of the SMPP beyond
the EW cosmological phase transition.
3.3 The baryogenesis problem
There is a large body of observational evidence that suggests that there is more
matter than antimatter in the Universe up to scales of the order of the Hubble