Primordial Black Holes and Cosmological Phase Transitions Report ...

More documents

Recommendations

Info

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

PBHs and Cosmological Phase Transitions 74 Figure 23: The energy density ε and pressure p (both divided by T 4 to compare to a free gas of massless quarks and gluons) as a function of T/Tc for the QCD transition in an LGT. The arrows mark the Stephan-Boltzmann result (Karsch et al., 2000; Ejiri, 2000). Figure 24: The square speed of sound c 2 s as a function of T/Tc for the QCD transition in a LGT (Gupta, 2003).
PBHs and Cosmological Phase Transitions 75 et al. (1999) had considered to fit the entropy density with s(T )= 2π2 3 T gHG +∆gΘ(T − Tc) RL + (1 − RL) 1 − 45 Tc γ T (137) which is valid for T > Tc. Here Θ and RL are given by equations (136) and (114) respectively, ∆g = gQGP − gHG and a good fit is obtained for 0.3 < γ < 0.4. We consider, for the rest of the text, γ =1/3. In Figure 22 we show the curve of s(T ) (labeled ‘lattice fit’). The other thermodynamic quantities (for T > Tc) can be derived from equation (137). Below Tc again is valid the equation for an ideal HG as in the case of the Bag Model (Schmid et al., 1999). Inserting the entropy fit given by equation (137) into equation (14) we obtain (Schmid et al., 1999) c 2 s ∝ 1 − Tc 1−γ T valid for T ≥ Tc. In order to recover c 2 s =1/3 when T ≫ Tc we consider c 2 s (138) 1 = 1 − 3 Tc 1−γ . (139) T For T = Tc we have c2 s = 0 and for T < Tc we get, once again, c2 s =1/3. In Figure 25 we show expression (139), as well as the results obtained for quenched QCD (Figure 24), for T ≥ Tc with Tc = 170 MeV. The analytic approach given by equation (139) and the numerical results obtained from quenched QCD (Figure 24) both show a similar behaviour, in particular, when T gets below ∼ 2Tc. It is useful to have also an expression for c2 s as a function of time t. Inserting expression (78) into expression (139) we obtain c 2 s (t) =1 1 − 3 R(t) 1−γ R(t−) (140) valid for t ≤ t− where t− corresponds to the beginning of the phase transition. Considering equation (86) or, alternatively, equation (71), we may write equation (140) in the form c 2 s (t) =1 3 2.3.3 Crossover 1/2 1−γ t 1 − . (141) t− Recent results provide strong evidence that the QCD transition is a Crossover, at least using staggered fermions, i.e., including fermionic fields in LGT (Aoki et al., 2006a,b).
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 8 and 9:
Page 10 and 11:
Page 12 and 13:
List of Tables 1 The Universe timel
Page 14 and 15:
Page 16 and 17:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42: PBHs and Cosmological Phase Transit
Page 91: PBHs and Cosmological Phase Transit
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Table 49 (continued). PBHs and Cosm
Page 223 and 224:
Table 49 (continued). Radiation EW
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
show all

Primordial Black Holes and Cosmological Phase Transitions Report ...

Create successful ePaper yourself

Delete template?

Save as template?