Using global gravitational potential weighted correlation function to constrain modified gravity models

We propose a new marked two-point correlation function weighted by the global gravitational potential as a probe for testing gravity models. Using the LCDM model based on general relativity (GR) as a reference, we investigate two representative modified gravity (MG) scenarios: f(R) gravity and nDGP. The mark used in this work, the global gravitational potential that is reconstructed from the galaxy distribution via the Poisson equation, is in contrast to the local property based mark (e.g., local galaxy number density or gravitational potential of host halo) used in previous studies. By applying two weighting schemes to quantify environment-dependent clustering, we find that this statistic is able to distinguish MG models from GR, with the signal being enhanced in regions corresponding to particular ranges of gravitational potential. These results indicate that the proposed statistic can serve as a useful complement to conventional clustering probes in future surveys, once observational effects and modeling uncertainties are properly taken into account.