Double copies of fermions as only gravitational interacting matter

Inspired by the recent progress in the field of scattering amplitudes, we discuss hypothetical particles which can be characterised as the double copies of fermions -- in the same way gravitons can be viewed as double copies of gauge bosons. As the gravitons, these hypothetical particles interact only through gravitational interactions. We present two equivalent methods for the computation of the relevant scattering amplitudes. The hypothetical particles can be massive and non-relativistic.