Srabilization of the dilaton
257
v
2
ReS
Figure 9.1. Representative two-condensate effective potential for ReS. The depths of the
minima and height of the maximum are very small.
the discussion to allow for Re S having non-minimal kinetic terms. This makes
little difference.)
However, the situation is drastically altered by several effects [5,6] not
included in the original treatment. First, the thermal energy density modifies
the Hubble parameter and if the thermal energy density is large compared to the
dilaton energy density, this can create sufficient 'friction' to allow the dilaton to
roll into the Re S = 2 minimum of V for a considerable range of initial values
of Re S. Second, the dilaton couples to the energy density of matter and gauge
fields and, third, Re S couples to the axion field, which is the imaginary part of S.
We shall focus here on the first of these effects.
For a homogeneous real scalar field tf> with minimal kinetic terms and
effective potential V (if», as in (7.33),
;p + 3Htb + V'(tf» = O.
(9.44)
We now want to allow for contributions to the Hubble parameter from the thermal
energy density of matter fields or radiation. We shaH take the field i f> to have a
potential of the form
V(tf» = Voe-l.1/>
(9.45)
in reduced Planck-scale units and shall discuss later how this relates to the dilaton
field. The pressure Pf3 and energy density pf3 of the matter fields or radiation
satisfy an equation of state
Pf3 = (E - l)pf3
(9.46)
where E = I for a matter-dominated universe and E = 4/3 for a radiationdominated universe during the rolling of i f> towards the minimum of its potential.
257
v
2
ReS
Figure 9.1. Representative two-condensate effective potential for ReS. The depths of the
minima and height of the maximum are very small.
the discussion to allow for Re S having non-minimal kinetic terms. This makes
little difference.)
However, the situation is drastically altered by several effects [5,6] not
included in the original treatment. First, the thermal energy density modifies
the Hubble parameter and if the thermal energy density is large compared to the
dilaton energy density, this can create sufficient 'friction' to allow the dilaton to
roll into the Re S = 2 minimum of V for a considerable range of initial values
of Re S. Second, the dilaton couples to the energy density of matter and gauge
fields and, third, Re S couples to the axion field, which is the imaginary part of S.
We shall focus here on the first of these effects.
For a homogeneous real scalar field tf> with minimal kinetic terms and
effective potential V (if», as in (7.33),
;p + 3Htb + V'(tf» = O.
(9.44)
We now want to allow for contributions to the Hubble parameter from the thermal
energy density of matter fields or radiation. We shaH take the field i f> to have a
potential of the form
V(tf» = Voe-l.1/>
(9.45)
in reduced Planck-scale units and shall discuss later how this relates to the dilaton
field. The pressure Pf3 and energy density pf3 of the matter fields or radiation
satisfy an equation of state
Pf3 = (E - l)pf3
(9.46)
where E = I for a matter-dominated universe and E = 4/3 for a radiationdominated universe during the rolling of i f> towards the minimum of its potential.