Fermion-antifermion mixing in gravitational fields

Mixing of fermion and antifermion states occurs in gravitational interactions, leading to non-conservation of fermion number above temperatures determined by the particle masses. We study the evolution of a $f,\bar{f}$ system and calculate the cross sections for the reactions $f\rightleftharpoons \bar{f}$. Their values are identical in both directions. However, if $\bar{f}$ changes quickly into a lighter antiparticle, then the reaction symmetry is broken, \emph{resulting in an increased production of matter over antimatter}.