We investigate in detail the interaction between the spin-${1/2}$ fields endowed with mass dimension one and the graviton. We obtain an interaction vertex that combines the characteristics of scalar-graviton and Diracs fermion-graviton vertices, due to the scalar-dynamic attribute and the fermionic structure of this field. It is shown that the vertex obtained obeys the Ward-Takahashi identity, ensuring the gauge invariance for this interaction. In the contribution of the mass dimension one fermion to the graviton propagator at one-loop, we found the conditions for the cancellation of the tadpole term by a cosmological counter-term. We calculate the scattering process for arbitrary momentum. For low energies, the result reveals that only the scalar sector present in the vertex contributes to the gravitational potential. Finally, we evaluate the non relativistic limit of the gravitational interaction and obtain an attractive Newtonian potential, as required for a dark matter candidate.
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