Cosmological cross-correlations and nearest neighbor distributions

Abstract

Cross-correlations between datasets are used in many different contexts in cosmological analyses. Recently, 𝑘-Nearest Neighbor Cumulative Distribution Functions (𝑘NN-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 𝑘NN-CDFs, 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 𝑘NN-CDFs 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.

Structure of cosmic web in non-linear regime: the nearest neighbour and spherical contact distributions

“…Paranjape & Alam (2020) introduced the Voronoi volume function and its sensitivity to the cosmological parameters. Banerjee & Abel (2020, 2021 introduced a new probe named the k-nearest neighbour (k-NN) distance from a Poisson distributed random points, which improves the constraints on the cosmological parameters. In this work, we use the spherical contact cumulative/probability distribution function (SC-CDF/PDF) which is complementary to the VP function.…”