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.
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Andrei Galiautdinov (2024) studied this question.
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