Positive-energy Dirac particles in cosmology

We provide general relativistic treatment of the single-component field described by Dirac's positive-energy wave equation of 1971. It is motivated by Bogomolny's proposal to regard that field as a possible candidate for dark matter. Our emphasis is on standard (flat) Friedmann-Robertson-Walker cosmology. The early universe is not considered, though there is a strong indication that the field may play a role in internally driven generation of cosmic anisotropy.