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We introduce an axion-inflation model embedded in the Left-Right symmetricextension of the SM in which $W_R$ is coupled to the axion. This model mergesthree milestones of modern cosmology, i.e., inflation, cold dark matter, andbaryon asymmetry. Thus, it can naturally explain the observed coincidencesamong cosmological parameters, i.e., $\eta_{B}\approx P_{\zeta}$ and$\Omega_{DM} \simeq 5~\Omega_{B}$. The source of asymmetry is spontaneous CPviolation in the physics of inflation, and the lightest right-handed neutrinois the cold dark matter candidate with mass $m_{N_1}\sim 1~GeV$. The introducedmechanism does not rely on the largeness of the unconstrained CP-violatingphases in the neutrino sector nor fine-tuned masses for the heaviestright-handed neutrinos. It has two unknown fundamental scales, i.e. scale ofinflation $\Lambda_{\rm inf}=\sqrt{HM_{Pl}}$ and left-right symmetry breaking$\Lambda_{F}$. Sufficient matter asymmetry demands $\Lambda_{\rminf}\approx\Lambda_{F}$. The baryon asymmetry and dark matter today areremnants of a pure quantum effect (chiral anomaly) in inflation, which, thanksto flavor effects, are memorized by cosmic evolution.

SU(2)$_R$ and its Axion in Cosmology: A common Origin for Inflation, Cold Sterile Neutrinos, and Baryogenesis