  There is no indication so far on the spin of dark matter particles. We
consider the possibility in this work that a spin-3/2 particle acts as dark
matter. Employing the approach of effective field theory, we list all possible
4-fermion effective interactions between a pair of such fields and a pair of
ordinary fermion fields. We investigate the implications of the proposal on the
relic density, the antiproton to proton flux ratio in cosmic rays, and the
elastic scattering off nuclei in direct detection. While the relic density and
flux ratio are sensitive to all interactions albeit at different levels, the
direct detection is only sensitive to a few of them. Using the observed data
and experimental bounds, we set constraints on the relation of couplings and
dark particle mass. In particular, we find that some mass ranges can already be
excluded by jointly applying the observed relic density on the one side and the
measured antiproton to proton flux ratio or the upper bounds from direct
detection on the other.
