Formazione di strutture cosmologiche con gravità modificata

On small and larger scales both, Universe is neither homogeneous nor isotropic: the Cosmological Principle has to be interpreted statistically. There must exist seeds around which, the matter is accreted through gravity, in order to form the cosmological structures we observe today. The goal that I set with this thesis work is to understand the cosmological structures formation using the Spherical Collapse model, at first in case of a flat E-dS model with a Newtonian approach, and after in particular with a gravity modification, using a Yukawa-like potential in the Lambda Cold Dark Matter model. I will see how cosmological density perturbation forms, expand and collapses with a constant barrier delta_c and I will also build the halo mass function in modified gravity, using Press and Schecter formalism. The results I have obtained using also Python's numerical simulation, tell us that the matter halos abundances are related to a certain amount of parameters of the model which we are using.