Degenerate Fermion Dark Matter from a Broken $U(1)_{\rm B-L}$ Gauge
  Symmetry
  The extension of the Standard model by assuming $U(1)_{\rm B-L}$ gauge
symmetry is very well-motivated since it naturally explains the presence of
heavy right-handed neutrinos required to account for the small active neutrino
masses via the seesaw mechanism and thermal leptogenesis. Traditionally, we
introduce three right handed neutrinos to cancel the $[U(1)_{\rm B-L}]^3$
anomaly. However, it suffices to introduce two heavy right-handed neutrinos for
these purposes and therefore we can replace one right-handed neutrino by new
chiral fermions to cancel the $U(1)_{\rm B-L}$ gauge anomaly. Then, one of the
chiral fermions can naturally play a role of a dark matter candidate. In this
paper, we demonstrate how this framework produces a dark matter candidate which
can address the so-called "core-cusp problem". As one of the small scale
problems that $\Lambda$CDM paradigm encounters, it may imply an important clue
for a nature of dark matter. One of resolutions among many is hypothesizing
that sub-keV fermion dark matter halos in dwarf spheroidal galaxies are in
(quasi) degenerate configuration. We show how the degenerate sub-keV fermion
dark matter candidate can be non-thermally originated in our model and thus can
be consistent with Lyman-$\alpha$ forest observation. Thereby, the small
neutrino mass, baryon asymmetry, and the sub-keV dark matter become
consequences of the broken B-L gauge symmetry.
