Real- and redshift-space halo clustering in $f(R)$ cosmologies
  We present two-point correlation function statistics of the mass and the
halos in the chameleon $f(R)$ modified gravity scenario using a series of large
volume N-body simulations. Three distinct variations of $f(R)$ are considered
(F4, F5 and F6) and compared to a fiducial $\Lambda$CDM model in the redshift
range $z \in [0,1]$. We find that the matter clustering is indistinguishable
for all models except for F4, which shows a significantly steeper slope. The
ratio of the redshift- to real-space correlation function at scales $> 20
h^{-1} \mathrm{Mpc}$ agrees with the linear General Relativity (GR) Kaiser
formula for the viable $f(R)$ models considered. We consider three halo
populations characterized by spatial abundances comparable to that of luminous
red galaxies (LRGs) and galaxy clusters. The redshift-space halo correlation
functions of F4 and F5 deviate significantly from $\Lambda$CDM at intermediate
and high redshift, as the $f(R)$ halo bias is smaller or equal to that of the
$\Lambda$CDM case. Finally we introduce a new model independent clustering
statistic to distinguish $f(R)$ from GR: the relative halo clustering ratio --
$\mathcal{R}$. The sampling required to adequately reduce the scatter in
$\mathcal{R}$ will be available with the advent of the next generation galaxy
redshift surveys. This will foster a prospective avenue to obtain largely
model-independent cosmological constraints on this class of modified gravity
models.
