<b>Abstract</b>— <p>Within the framework of the field theory of gravity, a theoretical description of dark matter is conducted. We associate dark matter with a unique generally covariant non-Abelian gauge field, which interacts only with gravitational field and does not interact with spinor field. The electromagnetic field is a singlet state of this gauge field. The mechanism for generating the mass of a generally covariant non-Abelian gauge field is inherent in the field itself and does not require the use of any additional fields. It is shown that the possibilities of observing and using a new energy source are mainly related with generally covariant law of energy conservation that holds in all cases.</p>