  Cold Dark Stars made of self-gravitating fermions in the degenerate limit are
constructed in General Relativity and in R-square gravity, $f(R)=R+\alpha R^2$.
The properties of the resulting Cold Dark Stars in both theories of gravity are
studied. It is found that the same gravitational potential is generated for
different election of the parameters of the model, such as the mass of the
fermion, the self-interacting strength or the value of $\alpha$, thus, a
possible confusion in the determination of the dark matter properties and the
favored theory of gravity might arise.
