Primordial dark matter halos from fifth-forces

In this thesis we investigate a possible formation mechanism of non-linear structures, such as primordial black holes or similar screened objects, within a modified gravity framework. In particular, these structures can form during radiation era and provide the current dark matter component of the Universe. We refer to a model consisting of a long range attractive fifth-force stronger than gravity, mediated by a light scalar field $\phi$ - which could be in principle dynamical dark energy of Coupled Quintessence - interacting with a non-relativistic $\psi$-particle. The latter is coupled to radiation and matter species only via usual gravity. By means of a dynamical system approach, we select the unique stable scaling solution of the phase space providing a radiation dominated era. Besides, after the introduction of the cosmological perturbation theory, we study the non-linear growth of the $\psi$ field density fluctuations in this epoch. The latter, being enhanced by the fifth interaction, in view of a field theory screening mechanisms that suppress the additional interaction, eventually collapse in stable and virialized structures, namely dark matter halos. We compare the theoretical predictions on the radius and the mass of the halos with experimental constraints on primordial black holes abundances, with an emphasis on their lensing signature in the solar mass window. In conclusion, we outline a viable scenario where the missing dark matter component of the universe might be completely supplied in form of dark halos.