  We show that in theories with nonminimal curvature-matter couplings up to
first order in the curvature, baryon number (B) conservation and CP are
automatically violated, provided that the curvature scalar and its gradient do
not vanish. Together with the associated gravitationally induced particle
creation in a cosmological framework, which is an essentially
out-of-equilibrium process, this implies that all of Sakharov's conditions are
satisfied in the simplest extension of General Relativity, without the need of
CPT violation. Here, derivatives of the curvature can be disregarded, thus
evading the potential problems associated with the Gravitational Baryogenesis
(GB) model in a cosmological context. Thanks to the particle creation pressure
and the trace anomaly, the curvature scalar is nonzero even in a
radiation-dominated Universe. Moreover, the trace anomaly or the energy density
of a massive scalar field can amplify the baryon asymmetry at very high
temperatures, even when the particle creation rate is very slow. As a result, a
baryon asymmetry compatible with observations and a huge CP violation can be
generated in the early Universe.

General Relativity and Quantum Cosmology