Fermionic dark matter and its self-interactions: from astrophysics to cosmology

We consider the problem of fermionic dark matter and study its effects across different time scales of the Universe, from today until early times of particle production. We work with alternative models to the cold, collisionless paradigm of DM: we focus on models including thermal velocities in the DM fluid (WDM), as well as self interacting extensions (SI-WDM). In the first part of this thesis, we start with the astrophysical analysis. We first analyze the formation and stability of O (keV) fermionic halos within a maximum entropy production approach, to then study how self-interactions affect the DM halos. We further perform an indirect detection analysis on such halos within a self interacting extension to a sterile neutrino WDM model. In the second part of the thesis, we consider the evolution of linear perturbations in cosmology under different SI-WDM scenarios at the level of the Boltzmann equations. We implement these modified models numerically and compare the results with observations on intragalactic scales. The results corresponding to the first part of this thesis, include the finding of a stable DM profile that develop a dense fermion-core (with applications to supermassive BH formation) surrounded by a dilute halo. Importantly, such a distinct core-halo profile can only form when the fermionic (quantum) nature of the DM particles is considered. Stronger indirect detection constraints for SI sterile neutrinos are found within the above fermionic halos. For the second part we develop a Boltzmann formalism as well as an application in CLASS for SI-WDM; calculate the power spectra for these cosmologies and compare with small scale observations, finding significantly relaxed bounds with respect to the standard WDM cosmology.