  The Standard Model Extension with the inclusion of gravity is studied in the
framework of the gravitational baryogenesis, a mechanism to generate the baryon
asymmetry based on the coupling between the Ricci scalar curvature and the
baryon current (\partial_\mu R)J^\mu. We show that, during the radiation era of
the expanding Universe, a non vanishing time derivative of the Ricci curvature
arises as a consequence of the coupling between the coefficients for the
Lorentz and CPT violation and Ricci's tensor. The order of magnitude for these
coefficients are derived from current bounds on baryon asymmetry.
