The mass distribution in the outskirts of clusters of galaxies as a probe of the theory of gravity

We show how $\varsigma$, the radial location of the minimum of the differential radial mass profile $M^{\prime }(r)$ of a galaxy cluster, can probe the theory of gravity. We derive $M^{\prime }(r)$ of the dark matter halos of galaxy clusters from N-body cosmological simulations that implement two different theories of gravity: standard gravity in the $\mathrm{\Lambda }$CDM model and $f(R)$. We extract 49169 dark matter halos in 11 redshift bins in the range $0\le z\le 1$ and in three different mass bins in the range $0.9