Improving Constraint on $Ω_{m}$ from SDSS Using Marked Correlation Functions

Abstract: Large-scale structure (LSS) surveys will increasingly provide stringent constraints on our cosmological models. Recently, the density-marked correlation function (MCF) has been introduced, offering an easily computable density-correlation statistic. Simulations have demonstrated that MCFs offer additional, independent constraints on cosmological models beyond the standard two-point correlation (2PCF). In this study, we apply MCFs for the first time to SDSS CMASS data, aiming to investigate the statistical information regarding clustering and anisotropy properties in the Universe and assess the performance of various weighting schemes in MCFs. Upon analyzing the CMASS data, we observe that, by combining different weights ($\alpha = [-0.2, 0, 0.2, 0.6]$), the MCFs provide a tight and independent constraint on the cosmological parameter $\Omega_m$, yielding $\Omega_m = 0.293 \pm0.006$ at the $1\sigma$ level, which represents a significant reduction in the statistical error by a factor of 3.4 compared to that from 2PCF. Our constraint is consistent with recent findings from the small-scale clustering of BOSS galaxies \cite{arXiv:2203.08999v2} within the 1$\sigma$ level. However, we also find that our estimate is lower than the Planck measurements by about 2.6$\sigma$, indicating the potential presence of new physics beyond the standard cosmological model if all the systematics are fully corrected. The method outlined in this study can be extended to other surveys and datasets, allowing for the constraint of other cosmological parameters. Additionally, it serves as a valuable tool for forthcoming emulator analysis on the Chinese Space Station Telescope (CSST).