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.