Testing modified gravity using a marked correlation function

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 $\mathrm{\Lambda }$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 $\mathrm{\Lambda }$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.