Fisher matrix for multiple tracers: the information in the cross-spectra

Abstract We derive general expressions for the multi-tracer Fisher matrix, both assuming that the cross-spectra are constrained by the auto-spectra, and also allowing for independent degrees of freedom in the cross-spectra. We show that, just like the ratios of power spectra, the independent degrees...

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Bibliographic Details
Published inJournal of cosmology and astroparticle physics Vol. 2022; no. 4; pp. 13 - 30
Main Authors Abramo, L. Raul, Ferri, João Vitor Dinarte, Tashiro, Ian Lucas
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.04.2022
Subjects
Degrees of freedom
galaxy clustering
Neutrons
Power spectra
power spectrum
redshift surveys
Tracers
Uncertainty
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Summary:Abstract We derive general expressions for the multi-tracer Fisher matrix, both assuming that the cross-spectra are constrained by the auto-spectra, and also allowing for independent degrees of freedom in the cross-spectra. We show that, just like the ratios of power spectra, the independent degrees of freedom of the cross-spectra are also not constrained by cosmic variance. Moreover, whereas the uncertainties in the ratios of power spectra decrease with the number density of the tracers as ∼ 1/ √n̅ , the uncertainties in the independent degrees of freedom of the cross-spectra decrease even faster, as ∼ 1/ n̅ . We also derive simple expressions for the optimal number of tracers in a survey.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2022/04/013