Fisher matrix for multiple tracers: the information in the cross-spectra
| Autor: | Abramo, L. Raul, Tashiro, Ian L., Ferri, João V. D. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1475-7516/2022/04/013 |
| Popis: | 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. Comment: 17 pages, 3 figures |
| Databáze: | arXiv |
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