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Title:
Uncorrelated modes of the non-linear power spectrum
Authors:
Hamilton, A. J. S.
Affiliation:
AA(JILA and Department of Astrophysical & Planetary Sciences, Box 440, University of Colorado, Boulder, CO 80309, USA)
Publication:
Monthly Notices of the Royal Astronomical Society, Volume 312, Issue 2, pp. 257-284. (MNRAS Homepage)
Publication Date:
02/2000
Origin:
MNRAS
MNRAS Keywords:
COSMOLOGY: THEORY, LARGE-SCALE STRUCTURE OF UNIVERSE
DOI:
10.1046/j.1365-8711.2000.03071.x
Bibliographic Code:
2000MNRAS.312..257H

Abstract

Non-linear evolution causes the galaxy power spectrum to become broadly correlated over different wavenumbers. It is shown that pre-whitening the power spectrum - transforming the power spectrum in such a way that the noise covariance becomes proportional to the unit matrix - greatly narrows the covariance of power. The eigenfunctions of the covariance of the pre-whitened non-linear power spectrum provide a set of almost uncorrelated non-linear modes somewhat analogous to the Fourier modes of the power spectrum itself in the linear, Gaussian regime. These almost uncorrelated modes make it possible to construct a near-minimum variance estimator and Fisher matrix of the pre-whitened non-linear power spectrum analogous to the Feldman-Kaiser-Peacock (FKP) estimator of the linear power spectrum. The paper concludes with summary recipes, in gourmet, fine and fastfood versions, of how to measure the pre-whitened non-linear power spectrum from a galaxy survey in the FKP approximation. An appendix presents FFTLog, a code for taking the fast Fourier or Hankel transform of a periodic sequence of logarithmically spaced points, which proves useful in some of the manipulations.

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