Primordial black holes formation in an early matter dominated era from the pre-big-bang scenario

We discuss the production of primordial black holes in an early matter dominated era, which typically takes place in string inspired early universe cosmological models. In particular, we consider a pre -big-bang scenario (extending previous results regarding formation in the radiation dominated era), where the enhancement of curvature perturbations is induced by a variation of the sound-speed parameter cs during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes, in the mass range relevant to dark matter, only for a small range of the parameter space. On the other hand, we find that a huge production of light primordial black holes may occur both in such matter dominated era and in the radiation dominated one.