Status of GUT baryogenesis
113
superpositions of those coming from the two 10s. This is sufficient to generate a
baryon asymmetry at the GUT symmetry-breaking scale [29].
The lesson to be learnt from these considerations is that a baryon asymmetry
can arise in such theories but that the energy scale at which it arises may be
much lower than the GUT scale. The magnitude of any such asymmetry depends
sensitively on the details of the particular model but, in many models, there is
ample room in parameter space to accommodate the observed asymmetry.
4.6 Status of GUT baryogenesis
The discussion in the two previous sections of baryogenesis using the baryonnumber non-conserving interactions of a GUT was based upon the assumption
that the superbeavy GUT gauge bosons or Higgs particles whose decays produce
the desired baryon asymmetry are, in the first place, in thermal equilibrium
and then, as the universe expanded and the temperature dropped, came out of
equilibrium when the condition (4.37) was satisfied. It is at least debatable
whether this assumption is well founded.
We shall see in chapter 7 that there are strong theoretical reasons, and some
support from observational data, for believing that the universe went through a
period of 'inflation', during which the scale factor grew by a factor of order
10' 2 7 , so that the observable universe evolved from a single Hubble volume. It
is, therefore, essential that the baryon asymmetry we observe was generated after
inflation: any asymmetry generated earlier would be so diluted by the inflation
as to render it utterly unobservable at the present time. This is the source of the
difficulty with the scenario envisaged hitherto. To generate the required amount
of inflation requires the inflaton potential to be rather flat: (the 'inflaton' (q,) is the
presumed field whose evolution determines how much inflation actually occurs).
This means that the mass of the inflaton is relatively low [30], in the range
m. ~ 10 13 _10 15 GeV
(4.] 16)
to account for the observed flatness and homogeneity of the universe and to solve
the horizon problem I. When it reaches the minimum of its potential, the inflaton
oscillates about its value at the minimum. As it does so, somehow, this lowentropy, cold universe evolves into a hot universe dominated by radiation. The
key question is: What is the temperature of this 'reheated' universe? This is a
vital question because the bound (4.116) means that, in some cases,
m. < 2mx
(4.117)
where m X is the mass of the particle whose decays generate the baryon
asymmetry. This is the case in the minimal SU(5) GUT, for example, where
I This is because m~ - V"(I/», and the double derivative is constrained by the condition (7.45) with
V(I/» satisfying (7.117).
113
superpositions of those coming from the two 10s. This is sufficient to generate a
baryon asymmetry at the GUT symmetry-breaking scale [29].
The lesson to be learnt from these considerations is that a baryon asymmetry
can arise in such theories but that the energy scale at which it arises may be
much lower than the GUT scale. The magnitude of any such asymmetry depends
sensitively on the details of the particular model but, in many models, there is
ample room in parameter space to accommodate the observed asymmetry.
4.6 Status of GUT baryogenesis
The discussion in the two previous sections of baryogenesis using the baryonnumber non-conserving interactions of a GUT was based upon the assumption
that the superbeavy GUT gauge bosons or Higgs particles whose decays produce
the desired baryon asymmetry are, in the first place, in thermal equilibrium
and then, as the universe expanded and the temperature dropped, came out of
equilibrium when the condition (4.37) was satisfied. It is at least debatable
whether this assumption is well founded.
We shall see in chapter 7 that there are strong theoretical reasons, and some
support from observational data, for believing that the universe went through a
period of 'inflation', during which the scale factor grew by a factor of order
10' 2 7 , so that the observable universe evolved from a single Hubble volume. It
is, therefore, essential that the baryon asymmetry we observe was generated after
inflation: any asymmetry generated earlier would be so diluted by the inflation
as to render it utterly unobservable at the present time. This is the source of the
difficulty with the scenario envisaged hitherto. To generate the required amount
of inflation requires the inflaton potential to be rather flat: (the 'inflaton' (q,) is the
presumed field whose evolution determines how much inflation actually occurs).
This means that the mass of the inflaton is relatively low [30], in the range
m. ~ 10 13 _10 15 GeV
(4.] 16)
to account for the observed flatness and homogeneity of the universe and to solve
the horizon problem I. When it reaches the minimum of its potential, the inflaton
oscillates about its value at the minimum. As it does so, somehow, this lowentropy, cold universe evolves into a hot universe dominated by radiation. The
key question is: What is the temperature of this 'reheated' universe? This is a
vital question because the bound (4.116) means that, in some cases,
m. < 2mx
(4.117)
where m X is the mass of the particle whose decays generate the baryon
asymmetry. This is the case in the minimal SU(5) GUT, for example, where
I This is because m~ - V"(I/», and the double derivative is constrained by the condition (7.45) with
V(I/» satisfying (7.117).