A theoretical approach to density-split clustering

TL;DR

This paper develops an analytical model for density-split galaxy clustering, comparing different statistical approximations and validating predictions against simulations, with implications for large-scale structure analysis.

Contribution

It introduces a novel analytical framework for density-split correlation functions using three approximation methods and validates the LDT approach against N-body simulations.

Findings

LDT outperforms log-normal in predicting density PDFs.

Model agrees with simulations on large scales within cosmic variance.

Uses only one degree of freedom for predictions.

Abstract

We present an analytical model for density-split correlation functions, that probe galaxy clustering in different density environments. Specifically, we focus on the cross-correlation between density-split regions and the tracer density field. We show that these correlation functions can be expressed in terms of the two-point probability density function (PDF) of the density field. We derive analytical predictions using three levels of approximation for the two-point PDF: a bivariate Gaussian distribution, a bivariate shifted log-normal distribution, and a prediction based on the Large Deviation Theory (LDT) framework. For count-in-cell densities, obtained through spherical top-hat smoothing, one can leverage spherical collapse dynamics and LDT to predict the density two-point PDF in the large-separation regime relative to the smoothing radius. We validate our model against dark matter N-body simulations in real space, incorporating Poisson shot noise and galaxy bias. Our results show that the LDT prediction outperforms the log-normal approximation, and agrees with simulations on large scales within the cosmic variance of a typical DESI DR1 sample, despite relying on only one degree of freedom.