Vacuum fluctuations in axion-dilaton cosmologies

We study axion-dilaton cosmologies derived from the low-energy string effective action. We present the classical homogeneous Friedmann-Rohertson-Walker solutions and derive the semiclassical perturbation spectra in the dilaton, axion, and moduli fields in the pre-big-bang scenario. By constructing the unique S-duality-invariant field perturbations for the axion and dilaton fields we derive S-duality-invariant solutions, valid when the axion field is time dependent as well as in a dilaton-vacuum cosmology. Whereas the dilaton and moduli fields have steep blue perturbation spectra (with spectral index n = 4) we find that the axion spectrum depends upon the expansion rate of the internal dimensions (0.54<n less than or equal to 4) which allows scale-invariant (n = 1) spectra. We note that for n less than or equal to 1 the metric is nonsingular in the conformal frame in which the axion is minimally coupled.