# 3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis

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Abstract : Context. Upcoming spectroscopic galaxy surveys are extremely promising to help in addressing the major challenges of cosmology, in particular in understanding the nature of the dark universe. The strength of these surveys, naturally described in spherical geometry, comes from their unprecedented depth and width, but an optimal extraction of their three-dimensional information is of utmost importance to best constrain the properties of the dark universe. Aims. Although there is theoretical motivation and novel tools to explore these surveys using the 3D spherical Fourier-Bessel (SFB) power spectrum of galaxy number counts Cℓ(k,k′), most survey optimisations and forecasts are based on the tomographic spherical harmonics power spectrum \hbox{$C^{(ij)}_\ell$}. The goal of this paper is to perform a new investigation of the information that can be extracted from these two analyses in the context of planned stage IV wide-field galaxy surveys. Methods. We compared tomographic and 3D SFB techniques by comparing the forecast cosmological parameter constraints obtained from a Fisher analysis. The comparison was made possible by careful and coherent treatment of non-linear scales in the two analyses, which makes this study the first to compare 3D SFB and tomographic constraints on an equal footing. Nuisance parameters related to a scale- and redshift-dependent galaxy bias were also included in the computation of the 3D SFB and tomographic power spectra for the first time. Results. Tomographic and 3D SFB methods can recover similar constraints in the absence of systematics. This requires choosing an optimal number of redshift bins for the tomographic analysis, which we computed to be N = 26 for zmed ≃ 0.4, N = 30 for zmed ≃ 1.0, and N = 42 for zmed ≃ 1.7. When marginalising over nuisance parameters related to the galaxy bias, the forecast 3D SFB constraints are less affected by this source of systematics than the tomographic constraints. In addition, the rate of increase of the figure of merit as a function of median redshift is higher for the 3D SFB method than for the 2D tomographic method. Conclusions. Constraints from the 3D SFB analysis are less sensitive to unavoidable systematics stemming from a redshift- and scale-dependent galaxy bias. Even for surveys that are optimised with tomography in mind, a 3D SFB analysis is more powerful. In addition, for survey optimisation, the figure of merit for the 3D SFB method increases more rapidly with redshift, especially at higher redshifts, suggesting that the 3D SFB method should be preferred for designing and analysing future wide-field spectroscopic surveys. CosmicPy, the Python package developed for this paper, is freely available at https://cosmicpy.github.io.
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Cited literature [20 references]

https://hal-cea.archives-ouvertes.fr/cea-01300572
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F. Lanusse, A. Rassat, J.-L. Starck. 3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis. Astronomy and Astrophysics - A&A, EDP Sciences, 2015, 578, pp.A10. ⟨10.1051/0004-6361/201424456⟩. ⟨cea-01300572⟩

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