Hypothesis of $P$-odd contribution to the gravitational interactions and its consequences

A generalized Lagrangian of spinor particles in a gravitational field containing $P$-odd terms is proposed. It is used to obtain a quasirelativistic equation of spinors in the field of a gravitational source with nonvanishing intrinsic angular momentum in both an inertial frame and in a frame rotating with the source. For these cases, the quasirelativistic Hamiltonian of a test body with nonzero intrinsic angular momentum is obtained in the classical limit; it is shown that the presence in the Hamiltonian of $P$-odd terms leads to the appearance of forces tlaat, depending on the orientation of the intrinsic angular momentum of the test body, are attractive or repulsive. It is noted that the $C$ noninvariance of the theory can in principle result in an evolution of the universe in which particles predominate over antiparticles. Other macroscopic consequences whose experimental verification would yield information about the values of the constants introduced in the theory are noted.