  A viable alternative to the dark energy as a solution of the cosmic speed up
problem is represented by Extended Theories of Gravity. Should this be indeed
the case, there will be an impact not only on cosmological scales, but also at
any scale, from the Solar System to extragalactic ones. In particular, the
gravitational potential can be different from the Newtonian one commonly
adopted when computing the circular velocity fitted to spiral galaxies rotation
curves. Phenomenologically modelling the modified point mass potential as the
sum of a Newtonian and a Yukawa like correction, we simulate observed rotation
curves for a spiral galaxy described as the sum of an exponential disc and a
NFW dark matter halo. We then fit these curves assuming parameterized halo
models (either with an inner cusp or a core) and using the Newtonian potential
to estimate the theoretical rotation curve. Such a study allows us to
investigate the bias on the disc and halo model parameters induced by the
systematic error induced by forcing the gravity theory to be Newtonian when it
is not. As a general result, we find that both the halo scale length and virial
mass are significantly overestimated, while the dark matter mass fraction
within the disc optical radius is typically underestimated. Moreover, should
the Yukawa scale length be smaller than the disc half mass radius, then the
logarithmic slope of the halo density profile would turn out to be shallower
than the NFW one. Finally, cored models are able to fit quite well the
simulated rotation curves, provided the disc mass is biased high in agreement
with the results in literature, favoring cored haloes and maximal discs. Such
results make us argue that the cusp/core controversy could actually be the
outcome of an incorrect assumption about which theory of gravity must actually
be used in computing the theoretical circular velocity.
