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 Standard Model in which <math display="inline"><msub><mi>W</mi><mi>R</mi></msub></math> 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., <math display="inline"><msub><mi>η</mi><mi mathvariant="sans-serif">B</mi></msub><mo>≈</mo><msub><mi>P</mi><mi>ζ</mi></msub></math> and <math display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mi>DM</mi></mrow></msub><mo>≃</mo><mn>5</mn><msub><mi mathvariant="normal">Ω</mi><mi mathvariant="sans-serif">B</mi></msub></math>. The source of asymmetry is spontaneous <math display="inline"><mi>C</mi><mi>P</mi></math> violation in the physics of inflation, and the lightest right-handed neutrino is the cold dark matter candidate with mass <math display="inline"><msub><mi>m</mi><msub><mi>N</mi><mn>1</mn></msub></msub><mo>∼</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. The introduced mechanism does not rely on the largeness of the unconstrained <math display="inline"><mi>C</mi><mi>P</mi></math>-violating phases in the neutrino sector or fine-tuned masses for the heaviest right-handed neutrinos. It has two unknown fundamental scales, i.e., scale of inflation <math display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>inf</mi></msub><mo>=</mo><msqrt><mrow><mi>H</mi><msub><mi>M</mi><mi mathsize="small">Pl</mi></msub></mrow></msqrt></math> and left-right symmetry breaking <math display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>F</mi></msub></math>. Sufficient matter asymmetry demands that <math display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>inf</mi></msub><mo>≈</mo><msub><mi mathvariant="normal">Λ</mi><mi>F</mi></msub></math>. Baryon asymmetry and dark matter today are remnants of a pure quantum effect (chiral anomaly) in inflation, which, thanks to flavor effects, has been memorized by cosmic evolution.