Indicator Power Spectra: Surgical Excision of Non-linearities and Covariance Matrices for Counts in Cells

TL;DR

This paper introduces indicator functions and their power spectra to identify density regions, correct for bias in large-scale spectra, and improve covariance matrix calculations for counts-in-cells, enhancing analysis of clustering data.

Contribution

It presents a novel application of indicator functions to characterize density dependence, correct bias in spectra, and compute covariance matrices for counts-in-cells, advancing clustering analysis methods.

Findings

Indicator-function spectra are biased versions of the linear spectrum on large scales.

The authors provide a first-principles calculation of this bias.

Application of these spectra enhances the linear theory reach and improves covariance estimates.

Abstract

We here introduce indicator functions, which identify regions of a given density in order to characterize the density dependence of clustering. After a general introduction to this tool, we show that indicator-function power spectra are biased versions of the linear spectrum on large scales. We provide a calculation from first principles for this bias, we show that it reproduces simulation results, and we provide a simple functional form for the translinear portion of the indicator-function spectra. We also outline two applications: first, these spectra facilitate surgical excision of non-linearity and thus significantly increase the reach of linear theory. Second, indicator-function spectra permit calculation of theoretical covariance matrices for counts-in-cells (CIC), facilitating parameter estimation with complementary CIC methods.