Journal Article

The full Fisher matrix for galaxy surveys

L. Raul Abramo

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 420, issue 3, pages 2042-2057
Published in print March 2012 | ISSN: 0035-8711
Published online February 2012 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.20166.x
The full Fisher matrix for galaxy surveys

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Starting from the Fisher matrix for counts in cells, we derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key step is the ‘classical approximation’, which allows us to write the inverse of the covariance of the galaxy counts in terms of the naive matrix inverse of the covariance in a mixed position-space and Fourier-space basis. We then compute the Fisher matrix for the power spectrum in bins of the 3D wavenumber , the Fisher matrix for functions of position (or redshift z) such as the linear bias of the tracers and/or the growth function and the cross-terms of the Fisher matrix that expresses the correlations between estimations of the power spectrum and estimations of the bias. When the bias and growth function are fully specified, and the Fourier-space bins are large enough that the covariance between them can be neglected, the Fisher matrix for the power spectrum reduces to the widely used result that was first derived by Feldman, Kaiser & Peacock. Assuming isotropy, a fully analytical calculation of the Fisher matrix in the classical approximation can be performed in the case of a constant-density, volume-limited survey.

Keywords: cosmology: theory; large-scale structure of the Universe

Journal Article.  11143 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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