Astroparticle Physics

208 9 The Early Universenet baryon numberattractive idea for several reasons. First, although the asymmetrybetween baryons and antibaryons today appears to belarge, i.e., lots of the former and none of the latter, at timescloser to the Big Bang, there were large amounts of both andthe relative imbalance was very small. This will be quantifiedin Sect. 9.5.2. Going back towards the Big Bang onewould like to think that nature’s laws become in some sensemore fundamental, and one would prefer to avoid the needto impose any sort of small asymmetry by hand.Furthermore, it now appears that the laws of natureallow, or even require, that a baryon asymmetry wouldarise from a state that began with a net baryon number ofzero. The conditions needed for this will be discussed inSect. 9.5.3.9.5.2 Size of the Baryon AsymmetryAlthough the universe today seems completely dominatedby baryons and not antibaryons, the relative asymmetry wasvery much smaller at earlier times. This can be seen roughlyby considering a time when quarks and antiquarks were allhighly relativistic, at a temperature of, say, T ≈ 1TeV,and suppose that since that time there have been no baryonnumber-violatingprocesses. The net baryon number in a co-moving volume R 3 is then constant, so one has(n b − n¯b )R3 = (n b,0 − n¯b,0 )R3 0 , (9.47)where the subscript 0 on the right-hand side denotes presentvalues. Today, however, there are essentially no antibaryons,so one can approximate n¯b,0 ≈ 0. The baryon–antibaryonasymmetry A is thereforebaryon-number-violatingprocessesbaryon–antibaryonasymmetryA ≡ n b − n¯b= n b,0 R03n b n b R 3 . (9.48)One can now relate the ratio of scale factors to the ratio oftemperatures, using the relation R ∼ 1/T. Therefore, onegetsA ≈ n b,0 T 3n b T03 . (9.49)Now one can use the fact that the number densities are relatedto the temperature. Equation (9.11) had shownn b ≈ T 3 , (9.50)n γ,0 ≈ T0 3 , (9.51)