Lima, R. de C.Guimaraes, T. M.Pereira, S. H. [UNESP]2022-11-302022-11-302022-09-19Journal Of High Energy Physics. New York: Springer, n. 9, 18 p., 2022.1029-8479http://hdl.handle.net/11449/237886The mass dimension one (MDO) fermionic field is built on a complete set of dual-helicity eigenspinors of the charge conjugation operator, which obeys the statistic of Fermi-Dirac. These spinors are a potential candidates for the description of dark matter. The redefinition of the dual structure of this object holds a local adjacent theory and completely satisfies the Lorentz invariance. In this work, we investigate important aspects of the interaction of this fermion with gravity in the light of a canonical formulation in ADM formalism. We construct an action via tetrad fields using a manifold on a family of space-like surfaces Sigma(t) that carries the MDO matter field, and additionally we propose a condition for the action to have a term associated with dark energy. We found the Hamiltonian and diffeomorphism constraints at the classical level for gravitational dynamics with the immersion of this material content in space-time, which leads us to the interpretation of the contribution of dark matter energy density, parallel to the lapse function of foliation and its directional flux of energy density in the hypersurface of manifold.18engClassical Theories of GravityEffective Field TheoriesModels of Quantum GravityArtigo10.1007/JHEP09(2022)132WOS:000855447400002