Chern-Simons Inflation and Baryogenesis
  We present a model of inflation based on the interaction between a
homogeneous and isotropic configuration of a U(1) gauge field and fermionic
charge density $\mathcal{J}_{0}$. The regulated fermionic charge density is
generated from a Bunch-Davies vacuum state using the methods of Koksma and
Prokopec \cite{Koksma:2009tc}, and is found to redshift as $1/a(\eta)$. The
time-like component of gauge field is sourced by the fermionic charge leading
to a growth in the gauge field $A(\eta)_{0}\sim a(\eta)$. As a result inflation
is dominated by the energy density contained in the gauge field and fermionic
charge interaction, $A_{0}\, \mathcal{J}^{0}$, which remains constant during
inflation. We also provide a mechanism to generate a net lepton asymmetry. The
coupling of a pseudo scalar to the Chern-Simons term converts the gauge field
fluctuations into lepton number and all three Sahkarov conditions are satisfied
during inflation. Finally, the rapid oscillation of the pseudo scalar field
near its minimum thermalizes the gauge field and ends inflation. We provide the
necessary initial condition on the gauge field and fermionic charge to
simultaneously generate enough e-folds and baryon asymmetry index.
