  String theory abounds with light scalar fields (the dilaton and various
moduli) which create a host of observational problems, and notably some serious
cosmological difficulties similar to the ones associated with the Polonyi field
in the earliest versions of spontaneously broken supergravity. We show that all
these problems are naturally avoided if a recently introduced mechanism for
fixing the vacuum expectation values of the dilaton and/or moduli is at work.
We study both the classical evolution and the quantum fluctuations of such
scalar fields during a primordial inflationary era and find that the results
are naturally compatible with observational facts. In this model, dilatons or
moduli within a very wide range of masses (which includes the SUSY-breaking
favored 1 TeV value and extends up to the Planck scale) qualify to define a
novel type of essentially stable ultra-weakly interacting massive particles
able to provide enough mass density to close the universe
