Constraints on self-interacting fermionic dark matter from galactic observables

The necessity of dark matter in the Universe was known since the ‘30s of the last century: its presence is indicated by cosmological and astrophysical observations. In fact, galaxy rotation curve cannot be explained by the visible matter. Within the dark matter particle paradigm many different kind of particles beyond the standard model have been suggested by scientists. Until today, much kind of particles have been proposed, from the three families of neutrinos to supersymmetric particles. In the chapter 1 I describe the evidences which led to the hypothesis of dark matter. I talk about the rotation curve of the galaxies and the gravitational lensing as evidence for the existence of the dark matter. In particular, I consider the case of the lensing caused by a system formed by the collision of two clusters of galaxies. Moreover, a general description of the Universe is provided, and its thermal history. In particular, some quantities necessary for the calculation of the relic density are presented. At the end of the chapter is considered the case of the CMB, and how the analysis of its anisotropies of temperature provides further proof of existence of dark matter. In the first part of chapter 2, candidates for the role of dark matter will be listed and described, highlighting the properties and characteristics of each of them. In addition, an alternative theory to dark matter will be discussed: the MOND, which consists of a modification of the gravitation on large scales of the universe. In the second part is described the particle hypothesis, according to which dark matter is made up of a particular type of massive particle, which interacts only weakly, called WIMP. In the chapter 3, I describe the RAR model, which is a model of semidegenerate system of fermions in spherical symmetry that attempts to explain dark matter in galaxies, analyzing the numerical results. After that, I describe a summary of the model for the case of the Milky Way, with the introduction of the cutoff parameter. Finally, I summarize the exposure of the orbits of the S-stars with DM at the center of the Galaxy, as an alternative to a SMBH scenario, results obtained in Becerra Vergara et al. In the chapter 4, I apply the RAR model to the self-interacting fermionic dark matter. I summarize the introduction of the RMF approximation (see paragraph 4.4), after considering the original RAR model for self-interacting dark matter with a sterile neutrino. I introduce the term Cv in the equations, summarizing the analysis of the numerical results. Finally, I apply the model to the Milky Way and to the relevant case of the Bright Clusters, taking into account the observational constraints, which are the original contributions to this Thesis.