Gravitational Leptogenesis and One-Loop Effective Actions


We investigate two aspects of inflation, the leading paradigm in modern cos- mology. In the first model we consider, the field that drives inflation is an axion, a real pseudoscalar with a shift symmetry. In this model the axion φ is coupled directly to a gravitational Chern-Simons term RR ̃, whose vacuum expectation value sources the gravitational anomaly in the lepton number cur- rent. The parameter space of the model is large enough to explain the observed matter asymmetry in the Universe. The second model consists of a scalar and pseudoscalar coupled to a heavy fermion in a classical electromagnetic back- ground. We calculate the one-loop effective action in the presence of slowly varying background fields, in order to investigate the radiative generation of terms like φFF ̃. Some aspects of the calculation are nonperturbative and ex- tend the Euler-Heisenberg effective action for QED. The result, though derived in flat spacetime rather than in an inflationary background, makes contact with axion inflation, and seeks to understand the underlying UV complete theories from which phenomenological models of inflation can arise.

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