216 The very early universe
with complexλ 1 ,λ 2 ) become important, and a substantial baryon asymmetry can
be produced. The scalar particles decay into ordinary quarks and leptons, transfer-
ring to them the generated baryon number. The Affleck–Dine mechanism can be
implemented at nearly any energy scale, even below 200 GeV.By suitable choice
of the parameters, one can explain almost any amount of baryon asymmetry. This
makes the Affleck–Dine scenario practically unfalsifiable and it is a very unattrac-
tive feature of this scenario.
More exotic possibilities have also been considered. Among them are baryo-
genesis via black hole evaporation and leptogenesis with very weakly coupled
right-handed Dirac neutrinos. Although at present the accepted wisdom favors lep-
togenesis, it is not clear which scenario was actually realized in nature. Therefore the
main lesson of this section is that there exist many ways to “solve” the baryogenesis
problem.
4.6.3 Topological defects
Topological defects do not occur in the Standard Model. However, they are a rather
generic prediction of theories beyond the Standard Model. Below we briefly discuss
why unified theories lead to topological defects and what kind of defects can be
produced in the early universe.
The Higgs mechanism has become an integral part of modern particle physics.
The main feature of this mechanism is the existence of scalar fields used to break
the original symmetry of the theory. Depending on the model, their Lagrangian can
be written as
Lφ=1
2
(∂αφ)(∂αφ)−λ
4(
φ^2 −σ^2) 2
, (4.230)
whereφ≡
(
φ^1 ,φ^2 ,...,φn)
is ann-plet of real scalar fields. Complex scalar fields
can be also rewritten in the form (4.230) if we use their real and imaginary parts.
For example, inU( 1 )gauge theory,φ=φ^1 +iφ^2 andn=2. The doublet of the
complex fields of electroweak theory corresponds ton= 4.
At very high temperatures symmetry is restored, that is,φ= 0 .As the universe
cools, phase transitions take place. As a result the scalar fields acquire vacuum
expectation values corresponding to the minimum of the potential in (4.230),
φ^2 =(
φ^1) 2
+
(
φ^2) 2
+···+
(
φn) 2
=σ^2.This vacuum manifoldMhas a nontrivial structure. For example, forn= 1 ,both
φ=σandφ=−σare states of minimal energy and so the vacuum manifold has
the topology of a zero-dimensional sphere,S^0 ={− 1 ,+ 1 }.InU( 1 )theory, the