Physical Foundations of Cosmology

120 The hot universe 3.6 Recombination The most important matter ingredients in thermodynamical processes after nucle- osynthesi ...

3.6 Recombination 121 most of the helium nuclei are converted into helium ions, we assume that the reaction He^2 ++e−He++γ (3.1 ...

122 The hot universe After most of the helium is converted into He+ions, the singly charged ions capture a second electron and b ...

3.6 Recombination 123 Therefore, for now, we neglect the excited hydrogen atoms and introduce the ion- ization fraction: Xe≡ ne ...

124 The hot universe a sequence of steps. However, even in cascading recombination, at least one very energetic photon is emitte ...

3.6 Recombination 125 thermal radiation e,p 2 P 2 S 1 S γ+γ Lα Fig. 3.9. to the nonthermalLαphotons. When the deviation from equ ...

126 The hot universe To expressX 2 Sin terms ofXe,we use the quasi-equilibrium condition for the intermediate 2Sreservoir; this ...

3.6 Recombination 127 the temperature drops belowT2450 K,thermal radiation no longer plays an essential role, and the quasi-equ ...

128 The hot universe equation (3.202) Saha approximation numerics 600 800 1000 1200 1400 redshift z ionization X e equation (3.2 ...

3.6 Recombination 129 cosmological expansion rate, which is an important factor in the kinetic description of nonequilibrium rec ...

130 The hot universe Finally, let us find out when exactly the universe becomes transparent to radi- ation. This occurs when the ...

4 The very early universe The laws of particle interactions are well established only below the energy cur- rently reached by ac ...

132 The very early universe its generation is a crucial element of inflationary cosmology. The general conditions under which th ...

4.1 Basics 133 4.1.1 Local gauge invariance Particles are interpreted as elementary excitations of fields. The field describing ...

134 The very early universe and Lagrangian (4.2), when we substituteDμfor∂μ, is invariant under local gauge transformations. The ...

4.1 Basics 135 Therefore, this diagram describes electron–positron annihilation with the emission of a photon. Because the photo ...

136 The very early universe charges are called “colors”). Lagrangian (4.9) is obviously invariant with respect to theglobalgauge ...

4.1 Basics 137 Problem 4.2Verify the transformation law forFμν.(HintTo simplify the calcu- lation, justify and use the following ...

138 The very early universe with detU= 1 .Therefore we can writeU(N)=U( 1 )×SU(N),and consider the localSU(N)gauge groups separa ...

4.2 Quantum chromodynamics and quark–gluon plasma 139 wheregsis the strong coupling constant,λC(whereC= 1 ,..., 8 )are the eight ...