Primordial Black Holes and Cosmological Phase Transitions Report ...

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PBHs and Cosmological Phase Transitions 182 log 10Βtk 0 -20 -40 -60 -80 n1.88, log 10t1s5 3 4 5 6 7 8 log10 tk 1 s Figure 98: The fraction of the universe going into PBHs in a radiation– dominated universe with a running–tilt power spectrum when n+ =1.88 and t+ = 10 5 s. Some values go over the ∼ 10 10 M⊙ line (cf. Figure 93). log 10Βtk 0 -20 -40 -60 -80 n2.00, log 10t1s7 3 4 5 6 7 8 log10 tk 1 s Figure 99: The fraction of the universe going into PBHs in a radiation– dominated universe with a running–tilt power spectrum when n+ =2.00 and t+ = 10 7 s. In this case the peak, and all non–zero values, fall on the > 10 10 M⊙ region (cf. Figure 93).

PBHs and Cosmological Phase Transitions 183 log 10Βtk -15 -15.5 -16 -16.5 -17 -17.5 n1.40, log 10t1s8 -10.5 -10 -9.5 -9 -8.5 -8 log10 tk 1 s Figure 100: The fraction of the universe going into PBHs for a running–tilt power spectrum with n+ =1.40 and t+ = 10 −8 s. The red line corresponds to the contribution from the EW Crossover while the black line represents the contribution from the radiation domination. The maximum difference between the two in β(tk) is of order unity ( 10 0.1 ). from the EW Crossover. 11.3 Electron–positron annihilation The cosmological electron–positron annihilation ocurred when the age of the universe was ∼ 1 s. Thus, the additional contribution from this epoch to the global value of β is more relevant when t+ ∼ 1 s. Integrating equation (288), with the threshold δc1 replaced by the appropriate values (e.g. Table 38), we find that the cases with a non–zero contribution from the electron–positron annihilation are in the range −2 ≤ log 10(t+/1s) ≤ 2 and 1.52 ≤ n+ ≤ 1.76, as shown on Table 43. Let us start with t+ = 1 s. In this case the contribution from the electron– positron annihilation epoch is almost equal in magnitude to the contribution from radiation (although with peaks at different epochs). In Figure 101a we show, as a first example, the case t+ = 1 s and n+ =1.56. From the radiation contribution we have βmax ∼ 10 −29 located at tk ∼ 10 −1.14 s and from the electron–positron annihilation contribution we have βmax ∼ 10 −34 located at tk ∼ 10 −0.07 s. As a second example we show in Figure 101b the case t+ = 1 s and n+ =1.62. Now, we have from the radiation contribution βmax ∼ 10 −10 located at tk ≈ 10 −1.2 s and from the electron–positron annihilation contribution βmax ∼ 10 −12 located at tk ≈ 10 −0.08 s. (contribution from radiation), then move to the red line (EW Crossover contribution) and, finally, move once again to the black line.

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Page 221 and 222: Table 49 (continued). PBHs and Cosm

Page 223 and 224: Table 49 (continued). Radiation EW










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