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We use two high resolution N-body simulations, one assuming generalrelativity and the other the Hu-Sawicki form of $f\left(R\right)$ gravity with$\vert \bar{f}_{R} \vert = 10^{-6}$, to investigate theconcentration--formation time relation of dark matter haloes. We stack haloesin logarithmically spaced mass bins to fit median density profiles and extractmedian formation times. At fixed mass, haloes in modified gravity are moreconcentrated than those in GR, especially at low masses and at low redshift,and do not follow the concentration--formation time relation seen in GR. Weassess the sensitivity of the relation to how concentration and formation timeare defined, as well as to the segregation of the halo population by the amountof gravitational screening. We find a clear difference between haloconcentrations and assembly histories displayed in modified gravity and thosein GR. Existing models for the mass--concentration--redshift relation that havegained success in cold and warm dark matter models require revision in$f\left(R\right)$ gravity.

The connection between halo concentrations and assembly histories: a probe of gravity?