Cosmological constraints from the density gradient weighted correlation function

Abstract

The mark weighted correlation function (MCF) $W(s,\mu )$ is a computationally efficient statistical measure which can probe clustering information beyond that of the conventional 2-point statistics. In this work, we extend the traditional mark weighted statistics by using powers of the density field gradient $|\nabla \rho /\rho {|}^{\alpha }$ as the weight, and use the angular dependence of the scale-averaged MCFs to constrain cosmological parameters. The analysis shows that the gradient based weighting scheme is statistically more powerful than the density based weighting scheme, while combining the two schemes together is more powerful than separately using either of them. Utilising the density weighted or the gradient weighted MCFs with $\alpha =0.5,1$, we can strengthen the constraint on ${\Omega }_m$ by factors of 2 or 4, respectively, compared with the standard 2-point correlation function, while simultaneously using the MCFs of the two weighting schemes together can be $1.25$ times more statistically powerful than using the gradient weighting scheme alone. The mark weighted statistics may play an important role in cosmological analysis of future large-scale surveys. Many issues, including the possibility of using other types of weights, the influence of the bias on this statistics, as well as the usage of MCFs in the tomographic Alcock-Paczynski method, are worth further investigations.

11 pages, 8 figures. Accepted by MNRAS

References in corpus (27)

• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS
• Properties of Dark Matter Haloes in Clusters, Filaments, Sheets and Voids
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in Fourier-space
• Theoretical Models of Dark Energy
• The darkness that shaped the void: dark energy and cosmic voids
• Cosmic web alignments with the shape, angular momentum and peculiar velocities of dark matter haloes
• A measurement of the Alcock-Paczynski effect using cosmic voids in the SDSS
• A marked correlation function for constraining modified gravity models
• Large-Scale Clustering of Cosmic Voids
• Cosmological constraints from the redshift dependence of the Alcock-Paczynski effect: application to the SDSS-III BOSS DR12 galaxies
• Breaking Halo Occupation Degeneracies with Marked Statistics
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: combining correlated Gaussian posterior distributions
• A Hybrid Deep Learning Approach to Cosmological Constraints From Galaxy Redshift Surveys
• What does the Marked Power Spectrum Measure? Insights from Perturbation Theory
• Measurement of marked correlation functions in SDSS-III Baryon Oscillation Spectroscopic Survey using LOWZ galaxies in Data Release 12
• Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data
• Cosmological constraints from the redshift dependence of the Alcock-Paczynski test and volume effect: galaxy two-point correlation function
• Non-parametric dark energy reconstruction using the tomographic Alcock-Paczynski test
• Cosmic Velocity Field Reconstruction Using AI
• The clustering of critical points in the evolving cosmic web
• Identification of Cosmic Voids as Massive Cluster Counterparts
• The redshift dependence of Alcock-Paczynski effect: cosmological constraints from the current and next generation observations
• Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Expansion History using the Genus Amplitude as a Standard Ruler
• Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Shape of the Matter Power Spectrum
• Using the Mark Weighted Correlation Functions to Improve the Constraints on Cosmological Parameters