Primordial Black Holes and Cosmological Phase Transitions Report ...

03.07.2013 Views
PBHs and Cosmological Phase Transitions 192 In Figure 106a we show the case t+ = 10 −4 s and n+ =1.40. In this case we have important contributions from the QCD transition (βmax ∼ 10 −9 in the case of a Bag Model, βmax ∼ 10 −14 in the case of a Lattice Fit and βmax ∼ 10 −75 in the case of a Crossover) and an almost negligible contribution from radiation (βmax ∼ 10 −97 ). We have also to consider new cases for which the contribution from radiation is negligible (β < 10 −100 for all tk, cases represented on Table 42 in cyan) but with some contribution from the QCD phase transition (cf. Table 44 – cases marked with ‘B’, and Table 45 – cases marked with ‘L’). In Figure 106b we show the case t+ = 10 −4 s and n+ =1.38, for which we have only meaningful contributions from the QCD Bag Model (βmax ∼ 10 −13 ) or from the QCD Lattice Fit (βmax ∼ 10 −22 ). In Figure 106c we show the case t+ = 10 −6 s and n+ =1.30, for which the only relevant contribution comes from the QCD Bag Model, with βmax ∼ 10 −69 . In the example of Figure 106d we show the case t+ = 10 −6 s and n+ = 1.40. Notice that we now have a visible contribution from radiation (βmax ∼ 10 −61 ) as well as an important contribution from the QCD Lattice Fit (βmax ∼ 10 −12 ). The contribution from the QCD Crossover (βmax ∼ 10 −74 ) is very small, compared with the others. In this case the QCD Bag Model is excluded, due to observational constraints. In Figure 106e we show, as a similar example, the case t+ = 10 −3 s and n+ =1.44, now with a more important contribution from the QCD Crossover (βmax ∼ 10 −43 ). The contribution from the Lattice Fit remains important (βmax ∼ 10 −11 ) and the QCD Bag Model remains excluded. Finally, in Figure 106f we show the case t+ = 10 −2 s and n+ =1.50. In this case we might have contributions from the QCD Bag Model (βmax ∼ 10 −9 ), from the QCD Lattice Fit (βmax ∼ 10 −11 ) or from the QCD Crossover (βmax ∼ 10 −28 ). We might have cases with simultaneous contributions from both QCD and EW transitions. Those are considered in Section 11.5. We might also have cases with simultaneous contributions from the QCD phase transition and from the electron–positron annihilation epoch. We have already presented two examples of these in Figures 102 and 103. 11.5 EW phase transition (MSSM) In this section we consider the contribution from the EW phase transition to the global value of β (in the context of the MSSM and taking into account the assumptions made at the end of Section 3.2.2). In Table 47 we point out the cases for which there is a non–negligible contribution from the EW phase transition. There are some cases allowed when one considers only the contribution from radiation but which must be excluded when one takes into account the EW phase transition. For example, the case t+ = 10 −9 s and n+ =1.36, represented in Figure 107. This case is not allowed in the context of a first order EW phase transition. However, if there is no such transition, or if this is not strong enough,

PBHs and Cosmological Phase Transitions 193 log 10Βtk log 10Βtk log 10Βtk 0 -20 -40 -60 -80 0 -20 -40 -60 -80 0 -20 -40 -60 -80 a n1.40, log 10t1s4 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 log10 tk 1 s c n1.30, log 10t1s6 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 log10 tk 1 s e n1.44, log 10t1s3 -6 -5 -4 -3 -2 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 n1.38, log 10t1s4 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 log10 tk 1 s d n1.40, log 10t1s5 -8 -7 -6 -5 -4 -3 log10 tk 1 s f n1.50, log 10t1s2 -5 -4 -3 -2 -1 0 log10 tk 1 s Figure 106: The fraction of the universe going into PBHs, during the QCD phase transition, in a universe with a running–tilt power spectrum when: (a) n+ = 1.40 and t+ = 10 −4 s; (b) n+ =1.38 and t+ = 10 −4 s; (c) n+ =1.30 and t+ = 10 −6 s; (d) n+ =1.40 and t+ = 10 −5 s; (e) n+ =1.44 and t+ = 10 −3 s; (f) n+ =1.50 and t+ = 10 −2 s (see Figure 104 for more details).

Page 1: CCM-Centro de Ciências Matemática

Page 4 and 5: Contents List of Figures vii List o

Page 6 and 7: PBHs and Cosmological Phase Transit



Page 12 and 13: List of Tables 1 The Universe timel


































































































Page 209: PBHs and Cosmological Phase Transit





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

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










transition

cosmological

pbhs

transitions

equation

formation

crossover

lattice

contribution

fluctuations

primordial

ccm.uma.pt

Primordial Black Holes and Cosmological Phase Transitions Report ...

Primordial Black Holes and Cosmological Phase Transitions Report ... ... View more Primordial Black Holes and Cosmological Phase Transitions Report ...

Delete template?

Save as template ?

Primordial Black Holes and Cosmological Phase Transitions Report ... Primordial Black Holes and Cosmological Phase Transitions Report ...