Primordial Black Holes and Cosmological Phase Transitions Report ...

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PBHs and Cosmological Phase Transitions 212 Table 52: Extended from Table 49 (cases in magenta), the ten cases with the largest contribution from the QCD Lattice Fit to β(tk). We have also indicated, in each case, the peak from the radiation contribution. In cases labeled with ‘E’ we might have contributions from the EW phase transition (Bag Model). In all cases a QCD Crossover is also allowed (labeled ‘C’). The QCD Bag Model is allowed for the cases labeled ‘B’ and must be excluded, due to observational constraints, in the other cases. For all cases the contribution from the electron– positron annihilation epoch is negligible. QCD Lattice Fit Radiation n+ log10 ( t+ 1s ) log tk,max 10 ( 1s ) βmax log10 ( tk,max 1s ) βmax Obs. 1.40 -6 -5.1 -13 -7.4 -38 E,C -5 -5.1 -12 – – C -4 -5.1 -14 – – B,C 1.42 -7 -5.1 -12 -8.5 -14 C -6 -5.1 -9 -7.5 -23 E,C -5 -5.1 -8 – – C -4 -5.1 -10 – – C 1.44 -3 -5.1 -11 – – C 1.50 -2 -5.1 -11 -3.3 -29 B,C 1.52 -2 -5.0 -8 -3.3 -19 C
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.
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CCM-Centro de Ciências Matemática
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Contents List of Figures vii List o
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PBHs and Cosmological Phase Transit
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List of Tables 1 The Universe timel
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