Dwarf spheroidal galaxies as degenerate gas of free fermions
  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.
