SU(2)$_R$ and its Axion in Cosmology: A common Origin for Inflation,
  Cold Sterile Neutrinos, and Baryogenesis
  We introduce an axion-inflation model embedded in the Left-Right symmetric
extension of the SM in which $W_R$ is coupled to the axion. This model merges
three milestones of modern cosmology, i.e., inflation, cold dark matter, and
baryon asymmetry. Thus, it can naturally explain the observed coincidences
among cosmological parameters, i.e., $\eta_{B}\approx P_{\zeta}$ and
$\Omega_{DM} \simeq 5~\Omega_{B}$. The source of asymmetry is spontaneous CP
violation in the physics of inflation, and the lightest right-handed neutrino
is the cold dark matter candidate with mass $m_{N_1}\sim 1~GeV$. The introduced
mechanism does not rely on the largeness of the unconstrained CP-violating
phases in the neutrino sector nor fine-tuned masses for the heaviest
right-handed neutrinos. It has two unknown fundamental scales, i.e. scale of
inflation $\Lambda_{\rm inf}=\sqrt{HM_{Pl}}$ and left-right symmetry breaking
$\Lambda_{F}$. Sufficient matter asymmetry demands $\Lambda_{\rm
inf}\approx\Lambda_{F}$. The baryon asymmetry and dark matter today are
remnants of a pure quantum effect (chiral anomaly) in inflation, which, thanks
to flavor effects, are memorized by cosmic evolution.
