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Articles Cosmology The Development of Baryon Asymmetry in the Early Universe (1980)
The Development of Baryon Asymmetry in the Early Universe (1980) |
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(1) Here we assume Maxwell-Boltzmann particles; the extra 
factors accounting for stimulated emission (Pauli exclusion effects) in the creation of bosons (fermions) are compensated by corresponding terms in the Boltzmann equation [4].
(2) We assume homogeneity and isotropy, so that 
.
(3) It is not necessary that these participate directly in 
-violating reactions.
(4) In the simple models discussed below, this phenomenon occurs if the universe is homogeneous and always cools faster than 
in practice any quark excess will be contained in baryons where their probability for collisions remains constant rather than falling as in a homogeneous expanding universe.
(5) This constraint applies only if no initial or final particles may mix with their antiparticles (as in the 
system). 
-violating mixing requires a difference 
in amplitudes rather than rates.
(6) Regardless of perturbation theory, violation is asymptotically suppressed by powers of 
where 
is the invariant mass of the initial state.
(7) This rather relevant point has also been noticed by Dolgov and Zeldovich [3], but was apparently neglected elsewhere.
(8) Strictly, 
should be averaged separately for the various terms of eq. (9); if 
is in kinetic equilibrium, however, the averages are equal. Note that we have implicitly assumed all produced and decaying 
to be exactly on their mass shells. However, particularly at high 
the mean collision time 
so that the resonance is collision broadened, and produced or decaying may be far off shell. The factor for inverse decays essentially arises from the fact that the incoming particles must subtend a sufficiently small angle to have invariant mass 
if produced are far off shell, the in DID should disappear.
(9) If 
as in footnote 8, then 
the universe expands sufficiently slowly for 
to relax to zero.
(10) In grand unified models where there exist absolutely stable particles more massive than nucleons which appear as simple replications (cf. e, 
), the mechanism described above should generate roughly equal concentrations of these as of nucleons: observational constraints on the total energy density of the universe then suggest that no such particles exist.
