Ultralight Fermionic Dark Matter
  Conventional lore from Tremaine and Gunn excludes fermionic dark matter
lighter than a few hundred eV, based on the Pauli exclusion principle. We
highlight a simple way of evading this bound with a large number of species
that leads to numerous non-trivial consequences. In this scenario there are
many distinct species of fermions with quasi-degenerate masses and no couplings
to the standard model. Nonetheless, gravitational interactions lead to
constraints from measurements at the LHC, of cosmic rays, of supernovae, and of
black hole spins and lifetimes. We find that the LHC constrains the number of
distinct species, bosons or fermions lighter than $\sim 500$ GeV, to be $N
\lesssim 10^{62}$. This, in particular, implies that roughly degenerate
fermionic dark matter must be heavier than $\sim 10^{-14}$ eV, which thus
relaxes the Tremaine-Gunn bound by $\sim 16$ orders of magnitude. Slightly
weaker constraints applying to masses up to $\sim100$ TeV exist from cosmic ray
measurements while various constraints on masses $\lesssim10^{-10}$ eV apply
from black hole observations. We consider a variety of phenomenological bounds
on the number of species of particles. Finally, we note that there exist
theoretical considerations regarding quantum gravity which could impose more
severe constraints that may limit the number of physical states to $N\lesssim
10^{32}$.
