In this paper we analyze a simple scenario in which Dark Matter ( DM ) consists of free fermions with mass m _ { f } .
We assume that on galactic scales these fermions are capable of forming a degenerate Fermi gas , in which stability against gravitational collapse is ensured by the Pauli exclusion principle .
The mass density of the resulting configuration is governed by a non-relativistic Lane-Emden equation , thus leading to a universal cored profile that depends only on one free parameter in addition to m _ { f } .
After reviewing the basic formalism , we test this scenario against experimental data describing the velocity dispersion of the eight classical dwarf spheroidal galaxies of the Milky Way .
We find that , despite its extreme simplicity , the model exhibits a good fit to the data and realistic predictions for the size of DM halos providing that m _ { f } \simeq 200 eV .
Furthermore , we show that in this setup larger galaxies correspond to the non-degenerate limit of the gas .
We propose a concrete realization of this model in which DM is produced non-thermally via inflaton decay .
We show that imposing the correct relic abundance and the bound on the free-streaming length constrains the inflation model in terms of inflaton mass , its branching ratio into DM and the reheating temperature .