Primordial Black Holes and Cosmological Phase Transitions Report ...

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$Kawasaki dynamic in continuum Math. Encounters XXXV ... - CCM$

PBHs and Cosmological Phase Transitions 214 Table 53: Extended from Table 49 (cases in red), the ten cases for which there is a larger contribution from the EW Bag Model to β(tk). We have also indicated, in each case, the peak from the radiation contribution. For some cases we might have also a contribution from the QCD Bag Model (labeled ‘B’) or from the QCD Lattice Fit (labeled ‘L’). The QCD Crossover as well as the electron–positron annihilation lead to negligible results for all cases. EW Bag Model Radiation n+ log 10( t+ 1s ) log 10( tk,max 1s ) βmax log 10( tk,max 1s ) βmax Obs. 1.32 -12 -10.6 -21 -13.6 -36 -11 -10.6 -18 -12.6 -49 -10 -10.6 -19 -11.5 -71 -9 -10.6 -23 – – 1.34 -12 -10.6 -12 -13.7 -18 -9 -10.6 -13 – – B -8 -10.6 -23 – – B 1.36 -8 -10.6 -13 – – B,L 1.38 -7 -10.6 -21 -8.5 -42 B,L 1.40 -7 -10.6 -13 -8.5 -24 B,L
PBHs and Cosmological Phase Transitions 215 Table 54: Extended from Table 49 (cases in cyan), the ten cases with the largerst contribution to β(tk) from the electron–positron annihilation epoch. We have also indicated, in each case, the peak from the radiation contribution. In the case t+ = 10 −1 s and n+ =1.60 we have a contribution from the QCD (Bag Model, Lattice Fit or Crossover – B,L,C). n+ electron–positron Radiation log10 ( t+ 1s ) log tk,max 10 ( 1s ) βmax log10 ( tk,max 1s ) βmax Obs. 1.60 -1 -0.1 -20 -2.2 -7 B,L,C 0 -0.1 -17 -1.2 -14 1.62 0 -0.1 -12 -1.2 -10 1 0.0 -16 – – 1.64 0 -0.1 -8 -1.2 -7 1 0.0 -12 – – 1.66 1 0.0 -8 – – 1.68 1 0.0 -6 – – 1.72 2 1.0 -8 – – 1.74 2 1.0 -6 – – 12.1.3 Electron–positron annihilation Other possible scenarios during which the sound speed might experience a reduction (besides cosmological phase transitions), are the cosmological particle annihilation periods. As an example, we considered the electron–positron annihilation epoch during which the sound speed might have decreased by about 20% (Section 4). This is a very interesting case because it corresponds to an epoch for which the horizon mass was ∼ 10 5 M⊙. We considered that, during this period, the sound speed has a ‘Crossover’–like profile. We have determined that a reduction of 20% on the value of the sound speed requires ∆T ≈ 0.115Tc (Section 4) and that this value leads to a reduction on the value of δc from 1/3 to ≈ 0.30 (Section 9, Figure 89). The electron–positron annihilation epoch is a smooth event with ∆g =3.5 (cf. Section 4), but not as smooth as the EW Crossover with ∆g = 1 (Section 3.2.1). So, we have non–negligible contributions to β (cf. Figure 101). Cut from Table 49, in Table 54 we present a list containing the ten highest contributions from the electron–positron annihilation epoch. In each case we have also show the contribution from radiation because it reaches important values for all ten cases.
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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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