Primordial Black Holes and Cosmological Phase Transitions Report ...

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

List of Tables 1 The Universe timeline . . . . . . . . . . . . . . . . . . . . . . . . 14 2 The best fit values for the ΛCDM model . . . . . . . . . . . . . . 22 3 The Scale Factor for different instants of time . . . . . . . . . . . 29 4 The three lepton families of the SMPP . . . . . . . . . . . . . . . 36 5 The three quark families of the SMPP . . . . . . . . . . . . . . . 37 6 Fundamental Bosons within the SMPP . . . . . . . . . . . . . . . 37 7 Mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 8 Baryons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 9 The SMPP particles and their supersymmetric MSSM partners . 44 10 The MSSM particles in terms of gauge eigenstates and mass eigenstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 11 Mass spectrum of the supersymmetric particles and the Higgs boson according to the SPS1a scenario . . . . . . . . . . . . . . . 48 12 The number of degrees of freedom for each kind of particle within the SMPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 13 The evolution of the number of degrees of freedom g(T ) in the Universe according to the SMPP . . . . . . . . . . . . . . . . . . 54 14 The number of degrees of freedom for each kind of particle within the MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 15 The evolution of the number of degrees of freedom g(T ) in the Universe according to the MSSM (SPS1a scenario) . . . . . . . . 57 16 The critcal temperature Tc for the QCD Crossover . . . . . . . . 76 17 The value of ∆R as a function of the number of degrees of freedom for the QCD Bag Model and for the QCD Lattice Fit . . . . . . 79 18 The width of the QCD Crossover in terms of temperature as a function of the parameter ∆T . . . . . . . . . . . . . . . . . . . . 83 19 The width of the QCD Crossover in terms of time as a function of the parameter ∆T . . . . . . . . . . . . . . . . . . . . . . . . . 84 20 The width of the QCD phase transition according to the Bag Model, Lattice Fit and Crossover when Tc = 170 MeV . . . . . . 85 21 The width of the EW Crossover in terms of temperature as a function of the parameter ∆T . . . . . . . . . . . . . . . . . . . . 96 22 The width of the EW Crossover in terms of time as a function of the parameter ∆T . . . . . . . . . . . . . . . . . . . . . . . . . . 97 23 The reduction of the speed of sound during the electron–positron annihilation and the corresponding values for the parameter ∆T 103 24 The width of the cosmological electron–positron annihilation in terms of temperature as a function of the parameter ∆T . . . . . 105 25 The width of the cosmological electron–positron annihilation in terms of time as a function of the parameter ∆T . . . . . . . . . 105 26 Classes of fluctuations for the QCD first–order phase transition . 111 27 Classes of fluctuations for the EW first–order phase transition . . 118 28 The intersection points δc2 = δc and δc1 = δc2, as a function of δc, for the QCD Bag Model . . . . . . . . . . . . . . . . . . . . . 126 xii
PBHs and Cosmological Phase Transitions xiii 29 The values of δAB, δBC, δc1 and δc2 for different values of x (when x>1) and δc according to the QCD Bag Model . . . . . . . . . . 128 30 The values of δBC, δCE and δc1 for different values of x (when y −1 < x < 1) and δc according to the QCD Bag Model . . . . . . 135 31 The values of δEF and δc1 for different values of x (when x < y −1 ) and δc according to the QCD Bag Model . . . . . . . . . . . . . . 139 32 The evolution of δc1 and δc2 as functions of time and as functions of the parameter x for the QCD Bag Model . . . . . . . . . . . . 142 33 The evolution of δc1 as a function of time for the QCD Crossover 146 34 The evolution of δcA, δc1 and δc2 as a function of time for the QCD Lattice Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 35 The lowest value of δc1,min for the EW Crossover with δc assuming different values . . . . . . . . . . . . . . . . . . . . . . . . . . 160 36 The evolution of δc1 as a function of time for a EW Crossover with ∆T =0.013Tc when δc =1/3 . . . . . . . . . . . . . . . . . 164 37 The evolution of δc1 and δc2 as functions of time and as functions of the parameter x for the EW Bag Model when δc =1/3 . . . . 166 38 The evolution of δc1 for the cosmological electron–positron annihilation with ∆T =0.115Tc and δc =1/3 . . . . . . . . . . . . . 169 39 The values of n2 and n3 when nmax =1.4 . . . . . . . . . . . . . 173 40 The different scenarios concerning the calculus of β . . . . . . . . 175 41 Different contributions to β . . . . . . . . . . . . . . . . . . . . . 177 42 The cases for which β> 10 −100 for a radiation–dominated Universe with a running–tilt power law spectrum . . . . . . . . . . . 181 43 The contribution to β from the electron–positron annihilation epoch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 44 The contribution to β from the QCD Bag Model . . . . . . . . . 188 45 The contribution to β from the QCD Lattice Fit . . . . . . . . . 189 46 The contribution to β from the QCD Crossover . . . . . . . . . . 190 47 The contribution to β from the EW Bag Model . . . . . . . . . . 194 48 Peaks of the curve β(tk) in the case n+ =1.36 and t+ = 10 −7 s . 199 49 The fraction of the universe going into PBHs during radiation domination and during cosmological phase transitions (the value of βmax for the various contributions) . . . . . . . . . . . . . . . 201 50 The ten cases with the largest contribution from the QCD Crossover to β(tk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 51 The ten cases with the largest contribution from the QCD Bag Model to β(tk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 52 The ten cases with the largest contribution from the QCD Lattice Fit to β(tk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 53 The ten cases with the largest contribution from the EW Bag Model to β(tk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 54 The ten cases with the largest contribution from the electron– positron annihilation epoch to β(tk) . . . . . . . . . . . . . . . . 215
Page 1: CCM-Centro de Ciências Matemática
Page 4 and 5: Contents List of Figures vii List o
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Table 49 (continued). PBHs and Cosm
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Table 49 (continued). Radiation EW
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Primordial Black Holes and Cosmological Phase Transitions Report ...

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