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.