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Upon embedding the axion-inflation in the minimal left-right symmetric gaugeextension of the SM with gauge group $SU(2)_L\times SU(2)_R \times U(1)_{B-L}$,[arXiv:2012.11516] proposed a new particle physics model for inflation. In thiswork, we present a more detailed analysis. As a compelling consequence, thissetup provides a new mechanism for simultaneous baryogenesis and right-handedneutrino creation by the chiral anomaly of $W_R$ in inflation. The lightestright-handed neutrino is the dark matter candidate. This setup has two unknownfundamental scales, i.e., the scale of inflation and left-right symmetrybreaking $SU(2)_R\times U(1)_{B-L}\rightarrow U(1)_{Y}$. Sufficient mattercreation demands the left-right symmetry breaking scale happens shortly afterthe end of inflation. Interestingly, it prefers left-right symmetry breakingscales above $10^{10}~GeV$, which is in the range suggested by thenon-supersymmetric SO(10) Grand Unified Theory with an intermediate left-rightsymmetry scale. Although $W_R$ gauge field generates equal amounts ofright-handed baryons and leptons in inflation, i.e. $B-L=0$, in the StandardModel sub-sector $B-L_{SM}\neq 0$. A key aspect of this setup is that $SU(2)_R$sphalerons are never in equilibrium, and the primordial $B-L_{SM}$ is conservedby the Standard Model interactions. This setup yields a deep connection betweenCP violation in physics of inflation and matter creation (visible and dark);hence it can naturally explain the observed coincidences among cosmologicalparameters, i.e., $\eta_{B}\simeq 0.3 P_{\zeta}$ and $\Omega_{DM}\simeq5\Omega_{B}$. The $SU(2)_R$-axion inflation comes with a cosmological smokinggun; chiral, non-Gaussian, and blue-tilted gravitational wave background, whichcan be probed by future CMB missions and laser interferometer detectors.

Chiral Anomaly in SU(2)${}_R$-Axion Inflation and the New Prediction for Particle Cosmology