2S2
Superstring cosmology
To avoid 4He and deuterium abundances being modified by the decay products
of the dilatinos, we should insist on the temperature Ts at the time of dilatino
decay being larger than 1 Me V :::: 10- 21 Mp. If we assume a radiation-dominated
universe during the period before the dilatons decay, then
.,.
t-1/2
3/2 M - I
(9.12)
's"'" S ,.." ms p
Thus, we require that
m s > IO- 14 Mp:::: 10 TeV.
(9.13)
We expect the gravitino mass m3/2, which controls the sizes of soft
supersymmetry breaking masses for the matter fields, to be not greater than about
10 Te V to solve the hierarchy problem. This bound can just be satisfied, especially
given that m S ,.." m3/2 is only a rough estimate. The same discussion applies to
the modulinos t;.
In any case, the cosmological problems that arise from the decays of light,
very weakly-interacting fermionic fields can be avoided if there is a period of
inflation, additional to the main period of inflation, to dilute this fermionic field
density. However, the reheat temperature after this period of inflation should not
be too high in order to avoid regeneration of the dilatino and modulino densities.
Thus, as discussed in section 85 for gravitinos, we should have a reheating
temperature
TR;S 10 9 GeV
(9.14)
so that any necessary regeneration of the baryon number density should occur
through low-temperature baryogenesis.
The cosmology of the dilaton S and moduli T; fields resembles that of the
Polonyi scalar field discussed in section 8.6, and much of the calculation given
there is unmodified. We shall focus on the dilaton field S but the discussion of the
moduli fields T; will be exactly similar. Consider first the case where the dilaton
field has started to oscillate before the inflaton decays. With a dilaton field energy
density at the end of inflation
Ps(t f) :::: !m~S2
(9.1S)
and assuming for the moment that the dilaton field does not decay, we find, as in
(8.11 S), that the requirement to avoid the dilaton field energy density dominating
the energy density of the universe today and producing too large an expansion rate
is
S:::: (I0-IS - 1O-16)msl/4.
(9.16)
For
ms ,.." m3/2 ,.." 100 GeV-1O TeV '" (I0-16_1O- 14 )Mp
(9.17)
we get
S :::: 10- 11 _10- 12
(9.18)
Superstring cosmology
To avoid 4He and deuterium abundances being modified by the decay products
of the dilatinos, we should insist on the temperature Ts at the time of dilatino
decay being larger than 1 Me V :::: 10- 21 Mp. If we assume a radiation-dominated
universe during the period before the dilatons decay, then
.,.
t-1/2
3/2 M - I
(9.12)
's"'" S ,.." ms p
Thus, we require that
m s > IO- 14 Mp:::: 10 TeV.
(9.13)
We expect the gravitino mass m3/2, which controls the sizes of soft
supersymmetry breaking masses for the matter fields, to be not greater than about
10 Te V to solve the hierarchy problem. This bound can just be satisfied, especially
given that m S ,.." m3/2 is only a rough estimate. The same discussion applies to
the modulinos t;.
In any case, the cosmological problems that arise from the decays of light,
very weakly-interacting fermionic fields can be avoided if there is a period of
inflation, additional to the main period of inflation, to dilute this fermionic field
density. However, the reheat temperature after this period of inflation should not
be too high in order to avoid regeneration of the dilatino and modulino densities.
Thus, as discussed in section 85 for gravitinos, we should have a reheating
temperature
TR;S 10 9 GeV
(9.14)
so that any necessary regeneration of the baryon number density should occur
through low-temperature baryogenesis.
The cosmology of the dilaton S and moduli T; fields resembles that of the
Polonyi scalar field discussed in section 8.6, and much of the calculation given
there is unmodified. We shall focus on the dilaton field S but the discussion of the
moduli fields T; will be exactly similar. Consider first the case where the dilaton
field has started to oscillate before the inflaton decays. With a dilaton field energy
density at the end of inflation
Ps(t f) :::: !m~S2
(9.1S)
and assuming for the moment that the dilaton field does not decay, we find, as in
(8.11 S), that the requirement to avoid the dilaton field energy density dominating
the energy density of the universe today and producing too large an expansion rate
is
S:::: (I0-IS - 1O-16)msl/4.
(9.16)
For
ms ,.." m3/2 ,.." 100 GeV-1O TeV '" (I0-16_1O- 14 )Mp
(9.17)
we get
S :::: 10- 11 _10- 12
(9.18)