Gravitational leptogenesis in axion inflation with SU(2) gauge field

We present an intrinsic leptogenesis mechanism in models of axion inflation with a classical SU(2) gauge field. The gauge fi eld is coupled to the axion with a Chern-Simons interaction and comprises a tiny fraction of the total energy, rho(YM)/rho(tot) less than or similar to is an element of(2). However, it has spin-2 fluuctuations which breaks the parity and leads to the generation of chiral gravitational waves during inflation. By the gravitational anomaly in SM, it naturally creates a net lepton number density, sufficient to explain the matter asymmetry. We show that this mechanism can generate the observed value of baryon to photon number density in a natural range of parameters and yet has a small chiral tensor power spectrum on large scales.