Cosmologically Degenerate Fermions
  Dark matter (DM) with a mass below a few keV must have a phase space
distribution that differs substantially from the Standard Model particle
thermal phase space: otherwise, it will free stream out of cosmic structures as
they form. We observe that fermionic DM psi in this mass range will have a
non-negligible momentum in the early Universe, even in the total absence of
thermal kinetic energy. This is because the fermions were inevitably more dense
at higher redshifts, and thus experienced Pauli degeneracy pressure. They fill
up the lowest-momentum states, such that a typical fermion gains a momentum ~
O(p_F) that can exceed its mass m_psi. We find a simple relation between m_psi,
the current fraction f_psi of the cold DM energy density in light fermions, and
the redshift at which they were relativistic. Considering the impacts of the
transition between nonrelativistic and relativistic behavior as revealed by
measurements of DNeff and the matter power spectrum, we derive qualitatively
new bounds in the f_psi-m_psi plane. We also improve existing bounds for f_psi
= 1 by an order of magnitude to m_psi=2 keV. We remark on implications for
direct detection and suggest models of dark sectors that may give rise to
cosmologically degenerate fermions.
