  A survey of solutions to the cosmological moduli problem in string theory.
The only extant proposal which may work is Intermediate Scale Inflation as
proposed by Randall and Thomas. Supersymmetry preserving dynamics which could
give large masses to the moduli is strongly constrained by cosmology and
requires the existence of string vacuum states possessing properties different
from those of any known vacuuum. Such a mechanism cannot give mass to the
dilaton unless there are cancellations between different exponentially small
contributions to the superpotential. Our investigation also shows that
stationary points of the effective potential with negative vacuum energy do not
correspond to stationary solutions of the equations of postinflationary
cosmology. This suggests that supersymmetry breaking is a requirement for a
successful inflationary cosmology.
