Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis

TL;DR

This study assesses the Fisher information in the galaxy angular power spectrum from SDSS DR5, revealing saturation at certain scales and implications for weak lensing analysis, especially regarding non-Gaussian noise effects.

Contribution

It provides the first detailed Fisher information analysis of SDSS galaxy data, highlighting the limited independent information at small scales and questioning Gaussian noise assumptions in weak lensing.

Findings

Fisher information saturates at multipole 300-2000.

Information at l=2000 is two orders of magnitude lower than Gaussian expectations.

Results suggest Gaussian noise assumptions may be invalid in weak lensing.

Abstract

We analyze the photometric redshift catalog of the Sloan Digital Sky Survey Data Release 5 (SDSS DR5) to estimate the Fisher information in the galaxy angular power spectrum with the help of the Rimes-Hamilton technique. It is found that the amount of Fisher information contained in the galaxy angular power spectrum is saturated at lensing multipole scale 300<= l <= 2000 in the redshift range 0.1<= photo-z <0.5. At l=2000, the observed information is two orders of magnitude lower than the case of Gaussian fluctuations. This supports observationally that the translinear regime of the density power spectrum contains little independent information about the initial cosmological conditions, which is consistent with the numerical trend shown by Rimes-Hamilton. Our results also suggest that the Gaussian-noise description may not be valid in weak lensing measurements.