Materia Oscura sotto forma di condensato di Bose-Einstein di un campo scalare

The currently accepted flat-$\Lambda$CDM model of Cosmology provides a good description of the evolution of the Universe and of structure formation on large scales. Despite this, it has issues in describing structure on galactic and sub-galactic scales, overpredicting the clustering of Dark Matter at this level. In particular $\Lambda$CDM predicts that Dark Matter halos will have a central cusp in the radial density profile, while observations are better fit by a cored distribution, i.e. one with a constant density in the central region. Furthermore, the most promising particle candidate for Dark Matter, the WIMP, has so far escaped detection. This motivates us to consider alternative models for Dark Matter, in particular in the form of an ultralight scalar particle which forms a Bose-Einstein condensate and can thus be described by a single macroscopic wave function. This form of Dark Matter can suppress clustering on small scales through the Heisenberg uncertainty principle and self-interaction, providing a natural scale of the order of $\sim 1$ kpc for the smallest structures that can be formed in this model. This can alleviate the small-scale problems of $\Lambda$CDM. The goal of this thesis is to study two aspects of this Dark Matter candidate: first, we study its effect on the overall evolution of the Universe, which sets constraints on the mass of the particle and the strength of its self-interaction by requiring consistency with known cosmological observables; secondly, we study how this model modifies structure formation, showing that it predicts halos with a cored density profile.