Confusing dark matter particle properties with modifications to General Relativity

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.