Chameleon $f(R)$ gravity on the Virgo cluster scale
  Models of modified gravity offer promising alternatives to the concordance
$\Lambda$CDM cosmology to explain the late-time acceleration of the universe. A
popular such model is $f(R)$ gravity, in which the Ricci scalar in the
Einstein-Hilbert action is replaced by a general function of it. We study the
$f(R)$ model of Hu & Sawicki (2007), which recovers standard General Relativity
in high density regimes, while reproducing the desired late-time acceleration
at cosmological scales. We run a suite of high resolution zoom simulations
using the ECOSMOG code to examine the effect of $f(R)$ gravity on the
properties of a halo that is analogous to the Virgo cluster. We show that the
velocity dispersion profiles can potentially discriminate between $f(R)$ models
and $\Lambda$CDM, and provide complementary analysis of lensing signal profiles
to explore the possibility to further distinguish the different $f(R)$ models.
Our results confirm the techniques explored by Cabre et al. (2012) to quantify
the effect of environment in the behavior of $f(R)$ gravity, and we extend them
to study halo satellites at various redshifts. We find that the modified
gravity effects in our models are most observable at low redshifts, and that
effects are generally stronger for satellites far from the center of the main
halo. We show that the screening properties of halo satellites trace very well
that of dark matter particles, which means that low-resolution simulations in
which subhalos are not very well resolved can in principle be used to study
satellite properties. We discuss observables, particularly for halo satellites,
that can potentially be used to constrain the observational viability of $f(R)$
gravity.
