The Bias of the Log Power Spectrum for Discrete Surveys

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), $A^{\ast }$ denotes the statistic analogous to the log density: $A^{\ast }$ 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 $A^{\ast }$ is biased with respect to the corresponding log spectrum for continuous fields, and to use $P_{A^{\ast }}(k)$ 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.

5 pages, 4 figures; published in MNRASL (here updated to published version)

References in corpus (3)

• Density distribution of the cosmological matter field
• Precision Prediction of the Log Power Spectrum
• Precision Prediction for the Cosmological Density Distribution

Cited by in corpus (4)

• Cosmic Web Dissection in Fuzzy Dark Matter Cosmologies
• An Ising model for galaxy bias
• Predicting the Sufficient-Statistics Power Spectrum for Galaxy Surveys: A Recipe for $P_{A\ast }(k)$
• Indicator Power Spectra: Surgical Excision of Non-linearities and Covariance Matrices for Counts in Cells