146 Thermal History of the Universe
by the time the Universe has cooled through the phase transition at푇GUT.Afterthat
the baryon number is absolutely conserved and further decrease in푁Bonly follows
the expansion. However, the photons are also bosons, so their absolute number is
not conserved and the value of휂may be changing somewhat. Thus, if we want to
confront the baryon production훥퐵required at푇GUTwith the present-day value of휂,
a more useful quantity is the baryon number per unit entropy푁B∕푆. Recall that the
entropy density of photons is
푠= 1. 80 푔∗(푇)푁훾 (6.115)from Equation (6.60). At temperature푇GUTthe effective degrees of freedom were
shown in Equation (6.46) to be 106.75 (in the standard model, not counting lepto-
quark degrees of freedom), so the baryon number per unit entropy is
푁B
푆=
훥퐵
1. 80 푔∗(푇GUT)
≃
훥퐵
180
. (6.116)
Clearly this ratio scales with푔∗−^1 (푇). Thus, to observe a present-day value of휂at about
the expected value the GUT should be chosen such that it yields
훥퐵=푔∗(푇GUT)
푔∗(푇 0 )
휂≃
106. 75
3. 36
휂≈ 1. 9 × 10 −^8 , (6.117)
making use of the푔∗(푇)values in Equations (6.67) and (6.46). This is within the pos-
sibilities of various GUTs.
One may of course object that this solution of thebaryosynthesisproblem is only
speculative, since it rests on the assumption that nature exhibits a suitable symmetry.
At the beginning of this section, we warned that the GUT symmetry did not necessarily
offer the best phase transition mechanism for baryosynthesis. The three conditions
referred to could perhaps be met at some later phase transition. The reason why the
GUT fails is to be found in the scenarios of cosmic inflation (Chapter 7). The baryon
asymmetry produced at푇GUTis subsequently washed out when the Universe reheats
to푇GUTat the end of inflation.
The search for another mechanism has turned to the electroweak phase transition
at about 100GeV. The ‘minimal standard model’ of electroweak interactions cannot
generate an asymmetry but, if the correct electroweak theory could be more general.
New possibilities arise if all three neutrino species oscillate and violate CP, or if one
turns to the ‘minimal supersymmetric standard model’. At the expanding interface
of the broken symmetry phase, the baryon–anti-baryon asymmetry could be gener-
ated via complex CP-violating reflections, transmissions and interference phenomena
between fermionic excitations. Thus the existence of baryons is an indication that
physics indeed has to go beyond the ‘minimal standard model’.
CPT Symmetry and Antigravity. A third discrete symmetry of importance istime
reversalT, or symmetry under inversion of the arrow of time. This is a mirror symmetry
with respect to the time axis, just as parity was a mirror symmetry with respect to the
space axes. All physical laws of reversible processes are formulated in such a way that
the replacement of time푡by−푡has no observable effect. The particle reactions in