Cosmological cross-correlations and nearest neighbor distributions

TL;DR

This paper introduces an extension of nearest neighbor distribution functions to analyze joint distributions and cross-correlations between cosmological datasets, demonstrating increased sensitivity to cosmological parameters and robustness in sparse regimes.

Contribution

It develops a framework for joint $k$-NN-CDF$ measurements, enhancing the detection of cross-correlations and cosmological information beyond traditional methods.

Findings

Joint $k$-NN-CDFs are sensitive to all connected N-point functions.

Nearest neighbor cross-correlations outperform traditional methods in sensitivity.

Robust detection of cross correlations in sparse samples.

Abstract

Cross-correlations between datasets are used in many different contexts in cosmological analyses. Recently, $k$-Nearest Neighbor Cumulative Distribution Functions ($k{\rm NN}$-${\rm CDF}$) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of nearest neighbor measurements to describe joint distributions of, and correlations between, two datasets. We describe the measurement of joint $k{\rm NN}$-${\rm CDF}$s, and show that these measurements are sensitive to all possible connected $N$-point functions that can be defined in terms of the two datasets. We describe how the cross-correlations can be isolated by combining measurements of the joint $k{\rm NN}$-${\rm CDF}$s and those measured from individual datasets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully nonlinear cosmological datasets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through nearest neighbor measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the nearest neighbor cross-correlations can robustly detect cross correlations between sparse samples -- the same regime where the two-point cross-correlation measurements are dominated by noise.