Fermionic Dark Matter: Physics, Astrophysics, and Cosmology

The nature of dark matter (DM) is one of the most relevant questions in modern astrophysics. We present a brief overview of recent results that inquire into a possible fermionic quantum nature of the DM particles, focusing mainly on the interconnection between the microphysics of the neutral fermions and the macrophysical structure of galactic halos, including their formation both in the linear and non-linear cosmological regimes. We discuss the general relativistic Ruffini-Arg\"uelles-Rueda (RAR) model of fermionic DM in galaxies, its applications to the Milky Way, the possibility that the Galactic center harbors a DM core instead of a supermassive black hole (SMBH), the S-cluster stellar orbits with an in-depth analysis of the S2's orbit including precession, the application of the RAR model to other galaxy types (dwarf, elliptic, big elliptic and galaxy clusters), and universal galaxy relations. All the above focusing on the model parameters constraints, most relevant to the fermion mass. We also connect the RAR model fermions with particle physics DM candidates, self-interactions, and galactic observables constraints. The formation and stability of core-halo galactic structures predicted by the RAR model and their relation to warm DM cosmologies are also treated. Finally, we briefly discuss how gravitational lensing, dynamical friction, and the formation of SMBHs can also probe the DM nature.