250
Superstring cosmology
only with difficulty, there can be adverse effects on inflation. This problem will
be discussed in section 9.3. On a slightly more positive note, the dilaton and
moduli fields with their flat potentials before supersyrrunetry breaking are possible
candidates for inftaton fields and this will be discussed in section 9.4.
The discussion up to this point in the chapter will assume that
compactification to four dimensions has already taken place. However, there
could be an era in the history of the universe during which all nine spatial
dimensions are still of comparable size. The cosmology of this era and how
it joins on to the era with just three large spatial dimensions will be discussed
in section 9.5. In particular, the question of why only three spatial dimensions
become large will be addressed.
All of this discussion is based on heterotic string theory. There are
also promising candidate theories based on type HA or type lIB string theory,
containing extended solutions referred to as 'D-branes'. The cosmology of Dbranes will be discussed in section 9.6.
Finally, in section 9.7 and section 9.8, we shall discuss two models for the
universe which allow there to have been an evolution of the universe prior to the
big bang. In the first of these models (pre-big-bang cosmology), the effect of
the (weakly-coupled) heterotic-string dilaton on the cosmological field equations
is exploited to obtain solutions with a growing positive Hubble parameter for
t < 0 driving inflation before the big bang. In the second model (the 'ekpyrotic'
universe), strongly coupled string theory is employed. Novel cosmology emerges
from the existence of an 11th dimension in the dual M-theory which will be
discussed in section 9.8.
9.2 Dilaton and moduli cosmology
Before discussing the cosmological implications of the existence of the dilaton
and moduli fields and their supersyrrunetric partners, we give some arguments
that allow the masses of these fields to be estimated [I]. The supergravity effective
potential is given by (2.147). It is convenient here to rewrite this in terms of the
F -term field
Fi = eG/2(G-I)~GJ
(9.1)
and its adjoint
F; == (F i ). = e G / 2 (G- 1 ){Gj
(9.2)
in the notation of (2.148). Then
v = F;FJGj - 3e G •
(9.3)
The mass of the dilaton (or modulus) field, denoted by f/> for the moment, is found
by differentiating the relevant part of (9.3), namely
v = F.~G: - 3e G + ....
(9.4)
Superstring cosmology
only with difficulty, there can be adverse effects on inflation. This problem will
be discussed in section 9.3. On a slightly more positive note, the dilaton and
moduli fields with their flat potentials before supersyrrunetry breaking are possible
candidates for inftaton fields and this will be discussed in section 9.4.
The discussion up to this point in the chapter will assume that
compactification to four dimensions has already taken place. However, there
could be an era in the history of the universe during which all nine spatial
dimensions are still of comparable size. The cosmology of this era and how
it joins on to the era with just three large spatial dimensions will be discussed
in section 9.5. In particular, the question of why only three spatial dimensions
become large will be addressed.
All of this discussion is based on heterotic string theory. There are
also promising candidate theories based on type HA or type lIB string theory,
containing extended solutions referred to as 'D-branes'. The cosmology of Dbranes will be discussed in section 9.6.
Finally, in section 9.7 and section 9.8, we shall discuss two models for the
universe which allow there to have been an evolution of the universe prior to the
big bang. In the first of these models (pre-big-bang cosmology), the effect of
the (weakly-coupled) heterotic-string dilaton on the cosmological field equations
is exploited to obtain solutions with a growing positive Hubble parameter for
t < 0 driving inflation before the big bang. In the second model (the 'ekpyrotic'
universe), strongly coupled string theory is employed. Novel cosmology emerges
from the existence of an 11th dimension in the dual M-theory which will be
discussed in section 9.8.
9.2 Dilaton and moduli cosmology
Before discussing the cosmological implications of the existence of the dilaton
and moduli fields and their supersyrrunetric partners, we give some arguments
that allow the masses of these fields to be estimated [I]. The supergravity effective
potential is given by (2.147). It is convenient here to rewrite this in terms of the
F -term field
Fi = eG/2(G-I)~GJ
(9.1)
and its adjoint
F; == (F i ). = e G / 2 (G- 1 ){Gj
(9.2)
in the notation of (2.148). Then
v = F;FJGj - 3e G •
(9.3)
The mass of the dilaton (or modulus) field, denoted by f/> for the moment, is found
by differentiating the relevant part of (9.3), namely
v = F.~G: - 3e G + ....
(9.4)