The connection between halo concentrations and assembly histories: a
  probe of gravity?
  We use two high resolution N-body simulations, one assuming general
relativity and the other the Hu-Sawicki form of $f\left(R\right)$ gravity with
$\vert \bar{f}_{R} \vert = 10^{-6}$, to investigate the
concentration--formation time relation of dark matter haloes. We stack haloes
in logarithmically spaced mass bins to fit median density profiles and extract
median formation times. At fixed mass, haloes in modified gravity are more
concentrated than those in GR, especially at low masses and at low redshift,
and do not follow the concentration--formation time relation seen in GR. We
assess the sensitivity of the relation to how concentration and formation time
are defined, as well as to the segregation of the halo population by the amount
of gravitational screening. We find a clear difference between halo
concentrations and assembly histories displayed in modified gravity and those
in GR. Existing models for the mass--concentration--redshift relation that have
gained success in cold and warm dark matter models require revision in
$f\left(R\right)$ gravity.
