Gravitational Baryogenesis: Problems and Possible Resolution

The coupling of baryonic current to the derivative of the curvature scalar, $R$, inherent to gravitational baryogenesis (GBG), leads to a fourth order differential equation of motion for $R$ instead of the algebraic one of General Relativity (GR). The fourth-order differential equation is generically unstable. We consider a possible mechanism of stabilization of GBG by modification of gravity, introducing an $R^2$-term into the canonical action of GR. It is shown that this mechanism allows for stabilization of GBG with bosonic and fermionic baryon currents. We have established the region of the model parameters leading to stabilization of $R$. Still, the standard cosmology would be noticeably modified.