Enhancing Cosmological Constraints by Two-dimensional <i>β</i>-cosmic-web Weighted Angular Correlation Functions

Abstract In this study, we investigate the potential of mark-weighted angular correlation functions, which integrate β -cosmic-web classification with angular correlation function analysis to improve cosmological constraints. Using SDSS DR12 CMASS-NGC galaxies and mock catalogs with Ω m varying from 0.25 to 0.40, we assess the discriminative power of different statistics via the average improvement in chi-squared, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>Δ</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> , across six redshift bins. This metric quantifies how effectively each statistic distinguishes between different cosmological models. Incorporating cosmic-web weights leads to substantial improvements. Using statistics weighted by the mean neighbor distance ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">nei</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) increases <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>Δ</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> by approximately 40%–130%, while applying inverse mean neighbor distance weighting ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">nei</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) yields even larger gains, boosting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>Δ</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> by a factor of 2–3 compared to traditional unweighted angular statistics. These enhancements are consistent with previous 3D clustering results, demonstrating the superior sensitivity of the β -weighted approaches. Our method, based on thin redshift slices, is particularly suitable for slitless surveys (e.g., Euclid, CSST) where redshift uncertainties limit 3D analyses. This study also offers a framework for applying marked statistics to 2D angular clustering.