• early universe
• inflation
• pre-big bang scenario
• primordial black holes
• string cosmology

In this thesis we examine the formation process of primordial black holes (PBHs) in the early universe. Particular emphasis is given to the Pre-Big Bang scenario, which suggests us the particular mechanism of formation studied in detail here, even if our model is also easily applicable to others, more standard, inflationary models.
The Pre-Big Bang scenario is a string cosmology model, which proposes an alternative inflationary mechanism to the standard potential-driven inflation; this is a kinetic-driven model, that happens in the pre-big bang phase, namely at t < 0.
The model is based on a low-energy 4-D effective string action that describes the graviton and the dilaton field. In this context the dilaton takes the role of the inflaton field, and drives the so-called super-inflationary solution from an empty and cold universe into a future singularity (i.e the big bang singularity); namely we have a pre-big bang solution dual to the standard post-big bang FRW solution, which has a singularity in the past.
Going toward the singularity one gets growing coupling and curvature, so the low-energy action is not sufficient to describe the model and one has to take into account two types of corrections: one equivalent to loop corrections in QFT, another (more unusual) called α' -corrections.
When one of the corrections (or both) becomes important we enter in the string phase, this can than be used to obtain a graceful-exit solution from pre- to post-big bang universe.
If in this solution we study the evolution of perturbations, both in the cases of α' and of loop corrections, we find a variation of the sound speed related to the tensor and to the scalar perturbations. The value of the sound speed that came out can be constant or varying in time, this is strongly related to the particular correction one has taken in account.
Motivated by the above pre-big bang model, we consider a generic case characterized by two (accelerated) inflationary phases, with (possible) different kinematic and characterized by the presence of a constant sound speed c_s , equal to one in the first phase and different from one (possible smaller) in the second.
These two phases are followed by a standard post-big bang decelerating phase, characterized by a sound speed c_s = 1.
We solve a Mukhanov-Sasaki like equation for all the phases and by a matching procedure we are able to obtain the complete perturbation spectra that depend in a non trivial way on c s and on the behaviour of the kinematic of the second phase.
We apply this machinery to the particular case of pre-big bang model; we sketch the scenario as three continuous phases: the dilaton-phase, the string-phase, and the post-big bang-phase. The first and the third phases are characterized by a c_s = 1, while the string phase by a constant c_s != 1, a priori lower or greater then one.
Using the obtained spectrum we then analyse the conditions for a suitable production of primordial black holes in order to explain all (of a non-negligible fraction) of the present dark matter.
In order to have a such suitable formation of PBHs one has to request an appropriate enhancement of the scalar power spectrum, enhancement that in our case is obtained by a sound speed variation.
Finally, we constrain the parameter space of the theory, essentially given by sound speed, duration of the string phase and the behaviour of the dilaton pump field in this phase, and obtain possible windows that permit a suitable formation of PBHs. To conclude, our analysis shows how is possible to form a suitable amount of PBHs, in order to explain the total or at least a fraction of the dark matter, in the Pre-Big Bang scenario.