The bias of the log power spectrum for discrete surveys. (12th December 2017)

• Record Type: Journal Article
• Authors: Repp, Andrew; Szapudi, István
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 475:Number 1(2018:Mar.)
• Page Start: L6
• Page End: L10
• Publication Date: 2017-12-12
• Subjects: cosmological parameters -- cosmology: miscellaneous -- cosmology: theory; Astronomy -- Research -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnrasl/slx201
• Languages: English
• ISSNs: 1745-3933

Abstract

Abstract: A primary goal of galaxy surveys is to tighten constraints on cosmological parameters, and the power spectrum P ( k ) is the standard means of doing so. However, at translinear scales P ( k ) is blind to much of these surveys' information – information which the log density power spectrum recovers. For discrete fields (such as the galaxy density), A * denotes the statistic analogous to the log density: A * is a 'sufficient statistic' in that its power spectrum (and mean) capture virtually all of a discrete survey's information. However, the power spectrum of A * is biased with respect to the corresponding log spectrum for continuous fields, and to use $P_{A^*}(k)$ to constrain the values of cosmological parameters, we require some means of predicting this bias. Here, we present a prescription for doing so; for Euclid -like surveys (with cubical cells 16 h −1 Mpc across) our bias prescription's error is less than 3 per cent. This prediction will facilitate optimal utilization of the information in future galaxy surveys.