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

We show that zeta, the radial location of the minimum in the differential radial mass profile M '(r) of a galaxy cluster, can probe the theory of gravity. We derived M '(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 Lambda CDM model, and f(R). We extracted 49169 dark matter halos in 11 redshift bins in the range 0 <= z <= 1 and in three different mass bins in the range 0.9 < M-200c/10(14)h(-1)M(circle dot) < 11. We investigated the correlation of zeta with the redshift and the mass accretion rate (MAR) of the halos. We show that zeta decreases from similar to 3R(200c) to similar to 2R(200c) when z increases from 0 to 1 in the Lambda CDM model. At z similar to 0.1, zeta decreases from 2.8R(200c) to similar to 2.5R(200c) when the MAR increases from similar to 10(4) h(-1) M(circle dot)yr(-1) to similar to 2 x 10(5) h(-1) M(circle dot)yr(-1). In the f(R) model, zeta is similar to 15% larger than in Lambda CDM. The median test shows that for samples of greater than or similar to 400 dark matter halos at z <= 0.8, zeta is able to distinguish between the two theories of gravity with a p-value less than or similar to 10(-5). Upcoming advanced spectroscopic and photometric programs will allow a robust estimation of the mass profile of enormous samples of clusters up to large clustercentric distances. These samples will allow us to statistically exploit zeta as probe of the theory of gravity, which complements other large-scale probes.