Cosmological CP Violation

Spinor fields are studied in infinite, topologically multiply connected Robertson-Walker cosmologies. Unitary spinor representations for the discrete covering groups of the spacelike slices are constructed. The spectral resolution of Dirac's equation is given in terms of horospherical elementary waves, on which the treatment of spin and energy is based in these cosmologies. The meaning of the energy and the particle-antiparticle concept is explained in the context of this varying cosmic background. Discrete symmetries, in particular inversions of the multiply connected spacelike slices, are studied. The violation of the unitarity of the parity operator, due to self-interference of P-reflected wave packets, is discussed. The violation of the CP and CPT invariance - already on the level of the free Dirac equation on this cosmological background - is pointed out.