4.6 Beyond the Standard Model 199doublet,a= 28 / 51 .On the other hand, it follows from (4.198) that the charges
Li−( 1 / 3 )Band, as a resultB−L,are conserved.
Topological transitions in the early universe can ensure equilibrium only if their
rate per fermion, equal to/nf∼α^4 wT(see ( 4.191)), exceeds the expansion rate
H∼T^2 ,that is, they are efficient ifT<α^4 w∼ 1012 GeV.Thus, even ifB+aL
were generated in the very early universe it would be washed out by topological
transitions at 10^12 Gev>T> 102 Gev. Hence ifB−L=0 then any pre-existent
baryon number does not survive. To explain baryon asymmetry, therefore, one has
to find a way to generateB−L=0 in the very early universe.The other possibility
is to generateB+aLduring a violent electroweak phase transition. However, this
does not look very realistic because the electroweak transition seems to be rather
smooth.
4.6 Beyond the Standard Model
Particle theories have been probed experimentally only to an energy scale of order a
few hundred GeV.If we want to learn anything about the early universe at energies
above 100 GeV,we inevitably have to rely on theories which are somewhere spec-
ulative. Fortunately they all have common features which may allow us to foresee
possible solution of important cosmological problems. Among these problems are
the origin of baryon asymmetry in the universe, the nature of dark matter and the
mechanism for inflation. We devote a separate chapter to inflation; here we concen-
trate on the first two questions. Since these questions cannot be answered within
the Standard Model, we are forced to go beyond it. In this section we begin by
outliningthe relevant general ideas behind the extensions of the Standard Model
and then discuss the ways in which these ideas can be implemented in cosmology.
Grand unification TheSU( 3 )×SU( 2 )×U( 1 )Standard Model is characterized
by the three coupling constantsgs,gandg′. They depend on the energy scale, and
the corresponding “fine structure constants”α≡g^2 / 4 πrun according to (4.29).
The strong interaction constantαsis given by (4.31).
In the case of theSU( 2 )group the coefficient f 1 ′( 1 )in (4.29) can be inferred
from (4.30). Forq>100 GeV all particles, including intermediate bosons, can
be treated as massless and the number of “colors”nin (4.30) is equal to 2.The
number of “flavors”fshould be taken to be equal tohalfthe number of left-handed
fermion doublets (not forgetting that there is a quark doublet for each color), that
is,f= 12 / 2 = 6 .Hence, for theSU( 2 )group,
f 1 ′( 1 )=1
12 π