Matter effects and CP violating neutrino oscillations with non-decoupling heavy neutrinos

The evolution equation for active and sterile neutrinos propagating in general anisotropic or polarized background environment is found and solved for a special case when heavy neutrinos do not decouple, resulting in non-unitary mixing among light neutrino states. Then new CP violating neutrino oscillation effects appear. In contrast to the standard unitary neutrino oscillations these effects can be visible even for two flavour neutrino transitions and even if one of the elements of the neutrino mixing matrix is equal to zero. They do not necessarily vanish with $delta m^{2} to 0$ and they are different for various pairs of flavour neutrino transitions ($ u_e to u_mu$), ($ u_mu to u_tau$), ($ u_tau to u_e$). Neutrino oscillations in vacuum and Earths matter are calculated for some fixed baseline experiments and a comparison between unitary and non-unitary oscillations are presented. It is shown, taking into account the present experimental constraints, that heavy neutrino states can affect CP and T asymmetries. This is especially true in the case of $ u_mu to u_tau$ oscillations.