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 196 βmax ∼ 10 −19 . Finally, we consider a few examples of a set of cases that have possible contributions from both the EW and QCD phase transitions (cf. Table 47, labeled BE, RBE, BLE, RBLE, RB ∗ LCE, and RB ∗ L ∗ CE). We start with the case t+ = 10 −7 s and n+ =1.34, represented in Figure 109a. In this case we have contributions from the EW phase transition (βmax ∼ 10 −61 ) and from the QCD phase transition (Bag Model – βmax ∼ 10 −33 , Lattice Fit – βmax ∼ 10 −68 ). In figures 109b and 109c we show the cases t+ = 10 −7 s and n+ =1.36 (see also Table 48 and Figure 110), and t+ = 10 −7 s and n+ =1.40, respectively. These are examples of cases characterized by contributions from the EW phase transition, QCD phase transition (Bag Model and Lattice Fit only) as well as from radiation. In particular, the second one (Figure 109c) shows very interesting values for β with two noticeable peaks (βmax ∼ 10 −13 from the EW and βmax ∼ 10 −9 from the QCD Bag Model or βmax ∼ 10 −17 from the QCD Lattice Fit). In Figure 109d we present the case t+ = 10 −6 s and n+ =1.44. In this case, the main contribution to β comes from radiation (βmax ∼ 10 −14 ), because the QCD Bag Model and Lattice Fit are excluded. We also have contributions from the EW phase transition and from the QCD phase transition (Crossover only). 11.6 Results In Table 49 we list the peaks of the curve β(tk), as well as their locations, for the various cases (and different scenarios) studied in Sections 11.1 to 11.5. The contribution from radiation assumes a radiation–dominated universe (δc =1/3 at all epochs) with the curve β(tk) showing a single peak. In addition we might also have contributions from the QCD phase transition, from the EW phase transition, or from the electron–positron annihilation epoch, each showing its own peak. If the peak from the radiation contribution is located near the epoch of a particular phase transition then it might be hidden by the corresponding peak. Consider, for example, the case n+ =1.44 and t+ = 10 −3 s (Figure 106e). In this case, we have non–negligible contributions from radiation and from the QCD Lattice Fit or from the QCD Crossover (the QCD Bag Model is excluded due to the observational constraints). Whatever the model one chooses to the QCD, the peak of the radiation contribution (black curve) remains hidden. Thus, in this case, the curve β(tk) exhibits only one peak. On table 49 there are other cases for which the peak from the radiation contribution is also hidden. For these cases we show the corresponding value of log 10 βmax inside brackets and labeled with ‘A’ (meaning Always hidden). As another example, consider the case n+ =1.36 and t+ = 10 −7 s (Figure 109b). In this case we might have one, two or three peaks, depending on the choosen scenario (see Table 48). This and other similar cases, are shown in Table 49, with the log 10 βmax value inside brackets and labeled ‘S’ (meaning Sometimes hidden).
PBHs and Cosmological Phase Transitions 197 log 10Βtk log 10Βtk log 10Βtk 0 -20 -40 -60 -80 0 -20 -40 -60 -80 0 -20 -40 -60 -80 a n1.28, log 10t1s10 -13 -12 -11 -10 -9 -8 log10 tk 1 s c n1.32, log 10t1s13 -18 -16 -14 -12 -10 -8 log10 tk 1 s e n1.30, log 10t1s12 -16 -14 -12 -10 -8 log10 tk 1 s log 10Βtk log 10Βtk log 10Βtk 0 -20 -40 -60 -80 0 -20 -40 -60 -80 0 -20 -40 -60 -80 b n1.32, log 10t1s9 -13 -12 -11 -10 -9 -8 log10 tk 1 s d n1.34, log 10t1s12 -18 -16 -14 -12 -10 -8 log10 tk 1 s f n1.32, log 10t1s10 -15 -14 -13 -12 -11 -10 -9 -8 log10 tk 1 s Figure 108: The fraction of the universe going into PBHs in a universe with a running–tilt power spectrum when: (a) n+ = 1.28 and t+ = 10 −10 s; (b) n+ = 1.32 and t+ = 10 −9 s; (c) n+ =1.32 and t+ = 10 −13 s; (d) n+ = 1.34 and t+ = 10 −12 s; (e) n+ = 1.30 and t+ = 10 −12 s; (f) n+ = 1.32 and t+ = 10 −10 s. The curves represent the contribution from the EW phase transition (red) and the contribution from radiation (black). Also shown (top of figures, in maroon) are the observational constraints.
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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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