  Analytical $f(R)$-gravity models introduce Yukawa-like corrections to the
Newtonian potential in the weak field limit. These models can explain the
dynamics of galaxies and cluster of galaxies without requiring dark matter. To
test the model, we have computed the pressure profile of 579 X-ray galaxy
clusters assuming the gas is in hydrostatic equilibrium within the potential
well of the modified gravitational potential. We have compared those profiles
with the ones measured in the foreground cleaned SMICA released by the Planck
Collaboration. Our results show that Extended Theories of Gravity explain the
dynamics of self-gravitating systems at cluster scales and represent an
alternative to dark matter haloes.
