Upon embedding the axion-inflation in the minimal left-right symmetric gauge extension of the SM with gauge group SU(2) L × SU(2) R × U(1)B−L, [1] proposed a new particle physics model for inflation. In this work, we present a more detailed analysis. As a compelling consequence, this setup provides a new mechanism for simultaneous baryogenesis and right-handed neutrino creation by the chiral anomaly of W R in inflation. The lightest right-handed neutrino is the dark matter candidate. This setup has two unknown fundamental scales, i.e., the scale of inflation and left-right symmetry breaking SU(2) R × U(1)B−L → U(1) Y . Sufficient matter creation demands the left-right symmetry breaking scale happens shortly after the end of inflation. Interestingly, it prefers left-right symmetry breaking scales above 1010 GeV, which is in the range suggested by the non-supersymmetric SO(10) Grand Unified Theory with an intermediate left-right symmetry scale. Although W R gauge field generates equal amounts of right-handed baryons and leptons in inflation, i.e. B − L = 0, in the Standard Model sub-sector B − LSM ≠ 0. A key aspect of this setup is that SU(2) R sphalerons are never in equilibrium, and the primordial B − LSM is conserved by the Standard Model interactions. This setup yields a deep connection between CP violation in physics of inflation and matter creation (visible and dark); hence it can naturally explain the observed coincidences among cosmological parameters, i.e., η B ≃ 0.3P ζ and ΩDM ≃ 5ΩB. The new 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. The SU(2) R -axion inflation comes with a cosmological smoking gun; chiral, non-Gaussian, and blue-tilted gravitational wave background, which can be probed by future CMB missions and laser interferometer detectors.