Chapter 9
Superstring cosmology
9.1 Introduction
For energies small compared to the string scale (which is of the order of
the Planck scale in weakly coupled heterotic string theories), heterotic string
theory in ten dimensions reduces to four-dimensional supergravity theory once
compactification of extra dimensions has taken place. Thus, the discussion
in chapter 8 also applies to heterotic string theory with special choices of
the superpotential and Kiihler potential derived from specific string theories.
However, there are other aspects of string theory cosmology that go beyond
supergravity cosmology.
Superstring theories contain massless (in the first instance) fields, referred
to as the 'dilaton' and, more generally. 'moduli', whose effective potential
is flat. These are a field theory manifestation of degeneracies of the string
vacuum. In particular, if the compactification of the theory from ten dimensions
to four dimensions occurs on a six-dimensional torus, certain of these moduli,
the 'T-moduli', correspond to the freedom (before non-perturbative effects are
considered) to vary continuously the radii of the torus along the associated
axes. Similarly, the (expectation value of the) dilaton S is associated with
the freedom to redefine the strength of the gravitational coupling. The dilaton
and moduli fields are expected to obtain masses on the electroweak scale
when supersymmetry breaking occurs and a non-trivial effective potential is
generated. The supersymmetric partners of the dilaton and moduli (the 'dilatino'
and 'modulinos') have a cosmology similar to the gravitino and can produce
unwelcome densities in the universe. The dilaton and moduli fields themselves
have a cosmology similar to the Polonyi field discussed in section 8.6 and can
produce excessive entropy by late decay. These problems will be discussed
in section 9.2 together with a possible solution through the thermal inflation
mechanism.
Another problem associated with the existence of the dilaton in particular is
the need for it to settle into a minimum of the effective potential. If this occurs
DOl: 10.1201/9780367806637-9
249
Superstring cosmology
9.1 Introduction
For energies small compared to the string scale (which is of the order of
the Planck scale in weakly coupled heterotic string theories), heterotic string
theory in ten dimensions reduces to four-dimensional supergravity theory once
compactification of extra dimensions has taken place. Thus, the discussion
in chapter 8 also applies to heterotic string theory with special choices of
the superpotential and Kiihler potential derived from specific string theories.
However, there are other aspects of string theory cosmology that go beyond
supergravity cosmology.
Superstring theories contain massless (in the first instance) fields, referred
to as the 'dilaton' and, more generally. 'moduli', whose effective potential
is flat. These are a field theory manifestation of degeneracies of the string
vacuum. In particular, if the compactification of the theory from ten dimensions
to four dimensions occurs on a six-dimensional torus, certain of these moduli,
the 'T-moduli', correspond to the freedom (before non-perturbative effects are
considered) to vary continuously the radii of the torus along the associated
axes. Similarly, the (expectation value of the) dilaton S is associated with
the freedom to redefine the strength of the gravitational coupling. The dilaton
and moduli fields are expected to obtain masses on the electroweak scale
when supersymmetry breaking occurs and a non-trivial effective potential is
generated. The supersymmetric partners of the dilaton and moduli (the 'dilatino'
and 'modulinos') have a cosmology similar to the gravitino and can produce
unwelcome densities in the universe. The dilaton and moduli fields themselves
have a cosmology similar to the Polonyi field discussed in section 8.6 and can
produce excessive entropy by late decay. These problems will be discussed
in section 9.2 together with a possible solution through the thermal inflation
mechanism.
Another problem associated with the existence of the dilaton in particular is
the need for it to settle into a minimum of the effective potential. If this occurs
DOl: 10.1201/9780367806637-9
249