Indicator power spectra: surgical excision of non-linearities and covariance matrices for counts in cells. Issue 1 (22nd October 2021)

• Record Type: Journal Article
• Authors: Repp, Andrew; Szapudi, István
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 509:Issue 1(2022)
• Page Start: 586
• Page End: 594
• Publication Date: 2021-10-22
• Subjects: cosmology: theory -- cosmology: miscellaneous -- methods: statistical; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stab3031
• Languages: English
• ISSNs: 0035-8711

Abstract

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.