Constraining f(R) gravity with Planck data on galaxy cluster profiles

Models of $f(R)$ gravity that introduce corrections to the Newtonian potential in the weak field limit are tested at the scale of galaxy clusters. These models can explain the dynamics of spiral and elliptical galaxies without resorting to dark matter. We compute the pressure profiles of 579 galaxy clusters assuming that the gas is in hydrostatic equilibrium within the potential well of the modified gravitational field. The predicted profiles are compared with the average profile obtained by stacking the data of our cluster sample in the Planck foreground clean map SMICA. We find that the resulting profiles of these systems fit the data without requiring a dominant dark matter component, with model parameters similar to those required to explain the dynamics of galaxies. Our results do not rule out that clusters are dynamically dominated by Dark Matter but support the idea that Extended Theories of Gravity could provide an explanation to the dynamics of self-gravitating systems and to the present period of accelerated expansion, alternative to the concordance cosmological model.