Physical Foundations of Cosmology

160 The very early universe where GF≡ 1 4 √ 2 g^2 MW^2 = π √ 2 αw^2 MW^2  1. 166 × 10 −^5 GeV−^2 (4.75) is Fermi coupling const ...

4.3 Electroweak theory 161 The gauge-invariant Yukawa coupling between scalars and fermions for the first lepton generation is L ...

162 The very early universe respectively,wherei= 1 , 2 ,3 is the generation index. The lower components are linear superposition ...

4.3 Electroweak theory 163 W+ W− νL eL ⎯ νR ∼ e⎯L Fig. 4.8. PandCoperations applied separately and in the Standard Model these s ...

164 The very early universe W− W+ W+ νR νR νL CP e⎯L eL+ e+R ∼ Fig. 4.9. The term describing the charged weak interactions for q ...

4.4 “Symmetry restoration” and phase transitions 165 As we will see,CPviolation plays a very important role in baryogenesis, en- ...

166 The very early universe following equation for ̄χ(t): χ ̄;α;α+V′(χ ̄)+ 1 2 V′′′(χ ̄) 〈 φ^2 〉 = 0 , (4.94) where the higher-o ...

4.4 “Symmetry restoration” and phase transitions 167 where [ˆ φx(t),πˆy(t) ] ≡φˆx(t)πˆy(t)−πˆy(t)φˆx(t) and Planck’s constant is ...

168 The very early universe using the results (4.101), we find that 〈 φ^2 (x) 〉 = 1 2 π^2 ∫ k^2 √ k^2 +m^2 φ(χ ̄) ( 1 2 +nk ) dk ...

4.4 “Symmetry restoration” and phase transitions 169 the mass is m^2 φ=V′′= 3 λ 0 χ ̄^2 +m^20. The divergent terms come to be mu ...

170 The very early universe In deriving this formula, we have changed the integration variablek→ωk/Tto express the result throug ...

4.4 “Symmetry restoration” and phase transitions 171 where the integralIis defined in (4.104) andVGis the energy density of the ...

172 The very early universe that symmetry is restored in the very early universe. Hence, if the mass of the Higgs particle did n ...

4.4 “Symmetry restoration” and phase transitions 173 V(χ) χ T>T 1 T=T 1 T 1 >T >Tc T=Tc T<Tc Fig. 4.10. 4.4.3 Symmet ...

174 The very early universe is separated from ̄χ=0 by a potential barrier of height, Vc= e^12 Tc^4 4 ( 4 π)^4 λ^3 Tc , (4.128) ...

4.4 “Symmetry restoration” and phase transitions 175 of the scalar field are about δφ= √〈 φ^2 〉 TT/ √ 24. For ̄χ<T/ √ 24 ,th ...

176 The very early universe χ V(χ) T 3 T 2 <T 3 T 1 <T 2 Fig. 4.11. 4.4.5 Electroweak phase transition The above considera ...

4.4 “Symmetry restoration” and phase transitions 177 Problem 4.21Verify thatft〈tt ̄〉=∂Vt/∂χ, ̄ where Vt≡ 3 × 4 ( − I(mt) 4 π^2 + ...

178 The very early universe Taking different values for the Higgs mass (10 GeV,30 GeV,100 GeV), find out when the potentialVeffb ...

4.4 “Symmetry restoration” and phase transitions 179 retained in (4.135) only whenmt(χ ̄)=Mtχ/χ ̄ 0 T, that is, for ̄χ(χ 0 /Mt ...