Marked statistics across the cosmic web: Environmental dependent clustering in modified gravity simulations

We study environment-dependent clustering using the marked correlation function applied to Hu-Sawicki $f(R)$ modified gravity simulations. This gravity theory enriches the structure formation by enhancing gravity in a scale-dependent form. By employing a multi-scale cosmic structure finder algorithm, we define the cosmic environments divided in: nodes, filaments, walls and voids. We find a stronger impact of modified gravity in nodes and filaments, which together dominate the information content by more than a factor of four relative to other environments. Combining environmental information further enhances the expected signal-to-noise ratio for CMASS- and DESI-like mock samples, particularly in configurations including filaments. Overall, marked correlation functions that incorporate environmental structure increase the information content by about a factor of two compared to standard density-based marks applied to the full galaxy sample. These results demonstrate the importance of environmental information, especially from filaments, in improving the sensitivity of galaxy clustering tests to deviations from GR in the $f(R)$ scenario.