  The problems of attempting inflationary model-building in a theory containing
a dilaton are explained. In particular, I study the shape of the dilaton
potential today and during inflation, based on a weakly-coupled heterotic
string model where corrections to the Kahler potential are assumed to be
responsible for dilaton stabilization. Although no specific model-building is
attempted, if the inflationary energy density is related to the scale of
gaugino condensation, then the dilaton may be stabilized close enough to
today's value that there is no significant change in the GUT scale coupling.
This can occur in a very wide range of models, and helps to provide some
justification for the standard predictions of the spectral index. I explain how
this result can ultimately be traced to the supersymmetry structure of the
theory.
