The role of the dark matter distribution in the structure formation

We review the most important ingredients that compose the halo model of structure formation, emphasizing on the role played by the density profile of dark matter (DM). The theoretical predictions of the so-called warm DM (WDM) and cold DM (CDM) cosmologies at small scales are discussed in terms of recent numerical simulations and current observational data coming from rotation curves of galaxies. We elaborate on the recently introduced Ruffini-Argüelles-Rueda (RAR) DM profile, which is obtained from the configuration of equilibrium of a self-gravitating system of massive fermions, hereafter "inos", and show that it can be a good candidate for WDM. A significant insight for this model might be inferred based on the analytical approach of the halo model, pointing out that there might have signals of quantum cores of galaxies on the non-linear matter power spectrum at small scales, which are however unfortunately inaccessible today with the current observational instruments. Upcoming surveys could test in the future the quantum features of galactic cores