Sterile Neutrino Dark Matter and Leptogenesis in Left-Right Higgs Parity
  The standard model Higgs quartic coupling vanishes at $(10^{9}-10^{13})$ GeV.
We study $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ theories that incorporate
the Higgs Parity mechanism, where this becomes the scale of Left-Right symmetry
breaking, $v_R$. Furthermore, these theories solve the strong CP problem and
predict three right-handed neutrinos. We introduce cosmologies where $SU(2)_R
\times U(1)_{B-L}$ gauge interactions produce right-handed neutrinos via the
freeze-out or freeze-in mechanisms. In both cases, we find the parameter space
where the lightest right-handed neutrino is dark matter and the decay of a
heavier one creates the baryon asymmetry of the universe via leptogenesis. A
theory of flavor is constructed that naturally accounts for the lightness and
stability of the right-handed neutrino dark matter, while maintaining
sufficient baryon asymmetry. The dark matter abundance and successful natural
leptogenesis require $v_R$ to be in the range $(10^{10}-10^{13})$ GeV for
freeze-out, in remarkable agreement with the scale where the Higgs quartic
coupling vanishes, whereas freeze-in requires $v_R \gtrsim 10^9$ GeV. The
allowed parameter space can be probed by the warmness of dark matter, precise
determinations of the top quark mass and QCD coupling by future colliders and
lattice computations, and measurement of the neutrino mass hierarchy.
