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Article
Report number	arXiv:2005.10384 ; CERN-TH-2020-044
Title	Beware of commonly used approximations : Part I. Errors in forecasts
Related title	Beware of commonly used approximations I: errors in forecasts
Author(s)	Bellomo, Nicola (Barcelona, IEEC ; Barcelona U., Dept. Fund. Phys.) ; Bernal, José Luis (Johns Hopkins U. ; Barcelona, IEEC ; Barcelona U., Dept. Fund. Phys.) ; Scelfo, Giulio (SISSA, Trieste ; INFN, Trieste ; IFPU, Trieste ; Padua U. ; Padua U., Astron. Dept. ; Barcelona, IEEC) ; Raccanelli, Alvise (CERN ; Barcelona, IEEC) ; Verde, Licia (Barcelona, IEEC ; ICREA, Barcelona)
Publication	2020-10-06
Imprint	2020-05-20
Number of pages	43
Note	43 pages, 9 figures. Matches the published version. \texttt{Multi\_CLASS} is now available at https://github.com/nbellomo/Multi_CLASS
In:	JCAP 2010 (2020) 016
DOI	10.1088/1475-7516/2020/10/016 (publication)
Subject category	astro-ph.CO ; Astrophysics and Astronomy
Abstract	In the era of precision cosmology, establishing the correct magnitude of statistical errors in cosmological parameters is of crucial importance. However, widely used approximations in galaxy surveys analyses can lead to parameter uncertainties that are grossly mis-estimated, even in a regime where the theory is well understood (e.g., linear scales). These approximations can be introduced at three different levels: in the form of the likelihood, in the theoretical modelling of the observable and in the numerical computation of the observable. Their consequences are important both in data analysis through e.g., Markov Chain Monte Carlo parameter inference, and when survey instrument and strategy are designed and their constraining power on cosmological parameters is forecasted, for instance using Fisher matrix analyses. In this work, considering the galaxy angular power spectrum as the target observable, we report one example of approximation for each of such three categories: neglecting off-diagonal terms in the covariance matrix, neglecting cosmic magnification and using the Limber approximation on large scales. We show that these commonly used approximations affect the robustness of the analysis and lead, perhaps counter-intuitively, to unacceptably large mis-estimates of parameters errors (from few $10\%$ up to few $100\%$) and correlations. Furthermore, these approximations might even spoil the benefits of the nascent multi-tracer and multi-messenger cosmology. Hence we recommend that the type of analysis presented here should be repeated for every approximation adopted in survey design or data analysis, to quantify how it may affect the results. To this aim, we have developed \texttt{Multi_CLASS}, a new extension of \texttt{CLASS} that includes the angular power spectrum for multiple (galaxy and other tracers such as gravitational waves) populations.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2020 IOP Publishing Ltd and Sissa Medialab

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