Marked clustering statistics in $f(R)$ gravity cosmologies

TL;DR

This study investigates how marked correlation functions in $f(R)$ gravity models differ from those in standard $ ext{Lambda}$CDM, revealing potential new probes for cosmic acceleration by analyzing environmental dependence in galaxy clustering.

Contribution

It demonstrates that galaxy marked correlation functions can distinguish $f(R)$ gravity models from $ ext{Lambda}$CDM on small scales, using N-body simulations and tailored marks.

Findings

Marked correlation functions differ significantly below 20 h^{-1} Mpc.

Environment-dependent marks reveal measurable differences between models.

Potential of marked correlation functions as probes for modified gravity.

Abstract

We analyse the two-point and marked correlation functions of haloes and galaxies in three variants of the chameleon $f(R)$ gravity model using N-body simulations, and compare to a fiducial $\Lambda$CDM model based on general relativity (GR). Using a halo occupation distribution prescription (HOD) we populate dark matter haloes with galaxies, where the HOD parameters have been tuned such that the galaxy number densities and the real-space galaxy two-point correlation functions in the modified gravity models match those in GR to within $1\sim3\%$. We test the idea that since the behaviour of gravity is dependent on environment, marked correlation functions may display a measurable difference between the models. For this we test marks based on the density field and the Newtonian gravitational potential. We find that the galaxy marked correlation function shows significant differences measured in different models on scales smaller than $r\lesssim 20~h^{-1}$ Mpc. Guided by simulations to identify a suitable mark, this approach could be used as a new probe of the accelerated expansion of the Universe.