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 210 Table 50: Extended from Table 49 (cases in green), the ten cases with the largest contribution from the QCD Crossover to β(tk). We have also indicated, in each case, the peak from the radiation contribution. In the case n+ =1.54 and t+ = 10 −2 we also have a non–negligible contribution from the QCD Lattice Fit. A label ‘ea’ indicates a non–negligible contribution from the electron–positron annihilation epoch (see text for more details). QCD Crossover Radiation n+ log 10( t+ 1s ) log 10( tk,max 1s ) βmax log 10( tk,max 1s ) βmax Obs. 1.46 -5 -4.5 -19 -6.4 -14 -4 -4.5 -19 -5.4 -23 -3 -4.5 -27 – – 1.48 -4 -4.5 -12 -5.4 -15 -3 -4.5 -18 – – 1.50 -4 -4.5 -8 -5.4 -9 -3 -4.5 -11 – – 1.52 -2 -4.4 -20 -3.3 -19 L 1.54 -2 -4.4 -13 -3.3 -13 ea 1.56 -2 -4.4 -9 -3.3 -8 ea
PBHs and Cosmological Phase Transitions 211 Table 51: Extended from Table 49 (cases in blue), the ten cases with the largest contribution from the QCD Bag Model 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 Lattice Fit is also allowed (labeled ‘L’) as well as the QCD Crossover (labeled ‘C’ for cases with non–negligible results). For all cases the contribution from the electron–positron annihilation epoch is negligible. QCD Bag Model Radiation n+ log 10( t+ 1s ) log 10( tk,max 1s ) βmax log 10( tk,max 1s ) βmax Obs. 1.38 -7 -5.3 -14 -8.5 -42 L,E -6 -5.3 -11 -7.4 -65 L -5 -5.3 -11 – – L -4 -5.3 -13 – – L 1.40 -8 -5.3 -13 -9.6 -16 L -7 -5.3 -9 -8.5 -24 L,E -4 -5.3 -9 – – L,C 1.42 -3 -5.3 -11 – – L,C 1.48 -2 -5.3 -14 -3.2 -44 L,C 1.50 -2 -5.3 -10 -3.3 -29 L,C peaks: i) βmax ∼ 10 −13 located at tk ∼ 10 −10.6 s – the contribution from the EW phase transition; ii) βmax ∼ 10 −24 located at tk ∼ 10 −8.5 s – the contribution from radiation; iii) βmax ∼ 10 −9 located at tk ∼ 10 −5.3 s – the contribution from the QCD Bag Model (or βmax ∼ 10 −18 located at tk ∼ 10 −5.1 s, in the case of a Lattice Fit). Cut from Table 49, in Table 52 we present a list with the ten largest contributions from the QCD Lattice Fit. In each case we have also indicated the contribution from radiation. For most of the ten cases the contribution from the QCD is by far much greater than the contribution from the radiation (the exception is the case t+ = 10 −7 s and n+ =1.42, for which we have similar contributions from both components). Values inside brackets correspond to situations for which the contribution from the QCD Lattice Fit hides the peak from the radiation contribution. A choice of a Bag Model, instead of a Lattice Fit, leads to results exceeding the observational constraints for most of the ten cases of Table 52. Only in cases labeled with ‘B’ the QCD Bag Model is also allowed. For all cases the QCD Crossover is allowed, giving non–negligible results.
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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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Page 221 and 222: Table 49 (continued). PBHs and Cosm
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