Physical Foundations of Cosmology

180 The very early universe and the symmetry is broken. The transition is a cross-over with no dramatic cos- mological consequen ...

4.5 Instantons, sphalerons and the early universe 181 a(E) b(E) qm E (^00) q instanton q sphaleron V −V Fig. 4.12. First, we neg ...

182 The very early universe InstantonsIn the special case ofE=0 (the particle is at rest at the local minimum of the potential) ...

4.5 Instantons, sphalerons and the early universe 183 probability that the particle gets energyEis given by the usual Boltzmann ...

184 The very early universe comes from the states which surmount the barrier classically. ForT>Esphthere is no exponential su ...

4.5 Instantons, sphalerons and the early universe 185 the metastable vacuum decays via quantum tunneling. If thermal fluctuation ...

186 The very early universe instanton “connects” the metastable vacuumφ(x)=0 to some (classically allowed) configurationφxwithV( ...

4.5 Instantons, sphalerons and the early universe 187 Forφx(τ)=φ(r ̃)(4.155) simplifies to the ordinary differential equation d^ ...

188 The very early universe with the instanton, is the unstablestaticsolution which depends only onthe spatial coordinatesx. For ...

4.5 Instantons, sphalerons and the early universe 189 inside the wall by a factorl/RI1 compared to(dφ/dr ̃)^2 andV.Therefore, ...

190 The very early universe in Minkowski spacetime. The picture described is a very close analog of subbarrier particle tunnelin ...

4.5 Instantons, sphalerons and the early universe 191 t r φ→φ 0 φ=const φ→ 0 Fig. 4.15. In particular, taking an arbitrary time- ...

192 The very early universe and (∂iU)U−^1 =−U ( ∂iU−^1 ) , (4.175) the variation of the first term in the integrand can be writt ...

4.5 Instantons, sphalerons and the early universe 193 wherer,θ,φare the spherical coordinates inxspace. Let us assume for simpli ...

194 The very early universe Thus, the field configuration interpolating between two topologically different vacua has a nonvanis ...

4.5 Instantons, sphalerons and the early universe 195 − 1 0 T= 0 instanton Msph sphaleron 1 T= 0 Fig. 4.16. The existence of ins ...

196 The very early universe This estimate is in good agreement with more elaborate calculations according to whichMsph7–13 TeV. ...

4.5 Instantons, sphalerons and the early universe 197 Fig. 4.17. The situation is very similar in non-Abelian gauge theories, wh ...

198 The very early universe andfgoes from 4 to 12 for three quark families, each of which is represented in three different colo ...

4.6 Beyond the Standard Model 199 doublet,a= 28 / 51 .On the other hand, it follows from (4.198) that the charges Li−( 1 / 3 )Ba ...