  We follow the evolution of the curvaton on superhorizon scales and check that
the spectral tilt of the curvaton perturbations is unchanged as the curvaton
becomes non-relativistic. Both inflation and pre-big bang cosmology can be
treated since the curvaton mechanism within the two scenarios works the same
way. We also discuss the amplitude of the density perturbations, which leads to
some interesting constrains on the pre-big bang scenario. It is shown that
within a SL(3,R) non-linear sigma model one of the three axions has the right
coupling to the dilaton and moduli to yield a flat spectrum with a high string
scale, if a quadratic non-perturbative potential is generated and an
intermediate string phase lasts long enough.
