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arXiv · 2112.01812

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

L. Raul Abramo·Ian L. Tashiro·João V. D. Ferri
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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 $\sim 1/\sqrt{\bar{n}}$, the uncertainties in the independent degrees of freedom of the cross-spectra decrease even faster, as $\sim 1/\bar{n}$. We also derive simple expressions for the optimal number of tracers in a survey.

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L. Raul Abramo, Ian L. Tashiro, João V. D. Ferri. 2021-12-03. Fisher matrix for multiple tracers: the information in the cross-spectra. https://doi.org/10.1088/1475-7516%2F2022%2F04%2F013

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