Sterile Neutrino Dark Matter in Left-Right Theories
  $SU(2)_L \times SU(2)_R$ gauge symmetry requires three right-handed neutrinos
($ N _i $), one of which, $N_1$, can be sufficiently stable to be dark matter.
In the early universe, $ W _R $ exchange with the Standard Model thermal bath
keeps the right-handed neutrinos in thermal equilibrium at high temperatures.
$N_1$ can make up all of dark matter if they freeze-out while relativistic and
are mildly diluted by subsequent decays of a long-lived and heavier
right-handed neutrino, $N_2$. We systematically study this parameter space,
constraining the symmetry breaking scale of $SU(2)_R$ and the mass of $N_1$ to
a triangle in the $(v_R,M_1)$ plane, with $v_R = (10^6 - 3 \times 10^{12})$ GeV
and $M_1 = (2\, {\rm keV} - 1 \, {\rm MeV)}$. Much of this triangle can be
probed by signals of warm dark matter, especially if leptogenesis from $N_2$
decay yields the observed baryon asymmetry. The minimal value of $v_R$ is
increased to $10^8 \, {\rm GeV}$ for doublet breaking of $SU(2)_R$, and further
to $10^9 \, {\rm GeV}$ if leptogenesis occurs via $N_2$ decay, while the upper
bound on $M_1$ is reduced to 100 keV. In addition, there is a component of hot
$N_1$ dark matter resulting from the late decay of $N_2 \rightarrow N_1 \ell^+
\ell^-$ that can be probed by future cosmic microwave background observations.
Interestingly, the range of $v_R$ allows both precision gauge coupling
unification and the Higgs Parity understanding of the vanishing of the Standard
Model Higgs quartic at scale $v_R$. Finally, we study freeze-in production of
$N_1$ dark matter via the $W_R$ interaction, which allows a much wider range of
$(v_R,M_1)$.
