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 76 Figure 25: The behaviour of the sound speed c 2 s as a function of T/Tc during the QCD transition according to the Lattice model (solid line – equation 139) and the numerical results obtained from quenched QCD. The dashed line represents the ideal gas case, i.e., c 2 s =1/3. When T = Tc the sound speed vanishes. The value of Tc for the QCD Crossover is not unique. Different observables lead to different numerical Tc values even in the continuum and thermodynamic limit. This is a well–known phenomenon on the water–vapour phase diagram. The peak of the renormalized chiral susceptibility predicts Tc = 151 MeV, whereas Tc based on the strange quark number susceptibility and Polyakov loops result in 175 MeV and 176 MeV, respectively (Aoki et al., 2006b). On Table 16 we summarize the results obtained by Aoki et al. (2006b) and Bernard et al. (2005), considering three quark flavours. The entropy density for a Crossover can be written as (e.g. Schmid et al., Table 16: The critcal temperature Tc for the QCD Crossover for different observables. Tc (MeV) Reference Observable 151 Aoki et al. (2006b) Chiral susceptibility 169 Bernard et al. (2005) Chiral susceptibility 175 Aoki et al. (2006b) Strange quark number susceptibility 176 Aoki et al. (2006b) Polyakov loops
PBHs and Cosmological Phase Transitions 77 cs 2 0.3 0.25 0.2 0.15 0.1 0.05 c b a 100 150 200 250 300 T MeV Figure 26: The sound speed c 2 s (T ) for the QCD Crossover with Tc = 170 MeV and different values for the parameter ∆T : (a) ∆T =0.1Tc, (b) ∆T =0.05Tc and (c) ∆T =0.02Tc. Notice that the sound speed decreases around Tc but does not reach zero (with the exception of the limiting case ∆T −→ 0 – see Figure 27). 1999; Schwarz, 1998) s(T )= 2π2 3 gHGT 45 1+ 1 2 ∆g gHG T − Tc 1 + tanh ∆T (142) where ∆g = gQGP −gHG and the value of ∆T must be choosen in order to fit the modeled results. When ∆T −→ 0 we recover the Bag Model, i.e., a first–order phase transition (Section 2.3.1). Both models coincide at temperatures far away from Tc (Schwarz, 1998). QCD Lattice data indicate that 0 ≤ ∆T
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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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Table 49 (continued). PBHs and Cosm
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Table 49 (continued). Radiation EW
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