We used the mark weighted correlation functions (MCFs), $W(s)$, to study the large scale structure of the Universe. We studied five types of MCFs with the weighting scheme $ρ^α$, where $ρ$ is the local density, and $α$ is taken as $-1,\ -0.5,\ 0,\ 0.5$, and 1. We found that different MCFs have very different amplitudes and scale-dependence. Some of the MCFs exhibit distinctive peaks and valleys that do not exist in the standard correlation functions. Their locations are robust against the redshifts and the background geometry, however it is unlikely that they can be used as ``standard rulers'' to probe the cosmic expansion history. Nonetheless we find that these features may be used to probe parameters related with the structure formation history, such as the values of $σ_8$ and the galaxy bias. Finally, after conducting a comprehensive analysis using the full shapes of the $W(s)$s and $W_{Δs}(μ)$s, we found that, combining different types of MCFs can significantly improve the cosmological parameter constraints. Compared with using only the standard correlation function, the combinations of MCFs with $α=0,\ 0.5,\ 1$ and $α=0,\ -1,\ -0.5,\ 0.5,\ 1$ can improve the constraints on $Ω_m$ and $w$ by $\approx30\%$ and $50\%$, respectively. We find highly significant evidence that MCFs can improve cosmological parameter constraints.
Instituto de Física Teórica UAM-CSIC（UAM-CSIC理论物理研究所）；Universidad Autónoma de Madrid（马德里自治大学）；University of Oxford（牛津大学）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学宇宙研究机构与物理数学国际研究中心卡弗里宇宙起源与演化前沿中心）；Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学宇宙研究机构与物理数学国际研究中心卡弗里宇宙起源与演化前沿中心数据驱动发现中心）
Improved Cosmological Constraints from Morphology-Based Marked Correlation Functions
School of Physics and Astronomy, Sun Yat-Sen University（中山大学物理学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理学院天文学系）；State Key Laboratory of Dark Matter Physics, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理学院暗物质物理全国重点实验室）；Key Laboratory for Particle Astrophysics and Cosmology (MOE)/Shanghai Key Laboratory for Particle Physics and Cosmology（粒子天体物理教育部重点实验室/上海粒子物理与宇宙学重点实验室）；Peng Cheng Laboratory（鹏城实验室）；CSST Science Center for the Guangdong–Hong Kong–Macau Greater Bay Area, SYSU（中山大学粤港澳大湾区空间望远镜科学中心）
Cosmological constraints from neighbor-density-weighted marked correlation functions
School of Physics and Astronomy, Sun Yat-Sen University（中山大学物理学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理学院天文学系）；State Key Laboratory of Dark Matter Physics, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理学院暗物质物理全国重点实验室）；Key Laboratory for Particle Astrophysics and Cosmology (MOE)/Shanghai Key Laboratory for Particle Physics and Cosmology（粒子天体物理学教育部重点实验室/上海粒子物理与天体物理重点实验室）；Peng Cheng Laboratory（鹏城实验室）；CSST Science Center for the Guangdong–Hong Kong–Macau Greater Bay Area, SYSU（中山大学中国空间站科学中心粤港澳大湾区分中心）
Using Global Gravitational Potential Weighted Correlation Function to Constrain Modified Gravity Models
State Key Laboratory of Dark Matter Physics, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院暗物质物理全国重点实验室）；Key Laboratory for Particle Astrophysics and Cosmology (MOE) / Shanghai Key Laboratory for Particle Physics and Cosmology（粒子天体物理与宇宙学教育部重点实验室/上海粒子物理与宇宙学重点实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）
