Testing modified gravity using a marked correlation function

TL;DR

This paper proposes using the marked correlation function to detect environment-dependent effects of modified gravity theories with chameleon screening, offering a new observational test distinguishing them from standard cosmology.

Contribution

It introduces the marked correlation function as a novel tool to capture environment dependence in structure formation for modified gravity models.

Findings

Marked correlation functions encode extra information about environment dependence.

Using local density or halo mass as marks enhances the ability to test modified gravity.

The method can be applied to observational data to distinguish between models.

Abstract

In theories of modified gravity with the chameleon screening mechanism, the strength of the fifth force depends on environment. This induces an environment dependence of structure formation, which differs from $\Lambda$CDM. We show that these differences can be captured by the marked correlation function. With the galaxy correlation functions and number densities calibrated to match between $f(R)$ and $\Lambda$CDM models in simulations, we show that the marked correlation functions from using either the local density or halo mass as the marks encode extra information, which can be used to test these theories. We discuss possible applications of these statistics in observations.