Euclid preparation. CXI. 6× 2pt analysis of Euclid's spectroscopic and photometric data sets
Abstract
In this paper we present cosmological parameter forecasts for the Euclid statistics, which include the galaxy clustering and weak lensing main probes together with previously neglected cross-covariance and cross-correlation signals between imaging-photometric and spectroscopic data. The aim is understanding the impact of such cross-terms on the expected Euclid performance. We adopted the Fisher information matrix approach to produce cosmological forecasts from Euclid, considering two different techniques known as the harmonic and hybrid approaches, respectively. In the first, we treat all the different Euclid probes in the same way, i.e., we consider only angular 2pt statistics for spectroscopic and photometric galaxy distributions, as well as for weak lensing, fully analyzing all their possible cross-covariances and cross-correlations in the spherical harmonic domain. In the second, thanks to lessons learned from the harmonic approach, we do not account for negligible cross-covariances between the 3D spectroscopic galaxy distribution and the 2D photometric/imaging data, but consider the combination of their cross-correlation with the autocorrelation signals. We find that both cross-covariance and cross-correlation signals between the two Euclid main probes, i.e., the spectroscopic galaxy sample and the photometric-imaging data, have a negligible impact on the cosmological parameter constraints and therefore on the Euclid performance. In the case of the hybrid approach, we attribute this result to the effect of the cross-correlation between weak lensing and photometric data, which is dominant with respect to other cross-correlation signals, and to the better performance of the full anisotropic 3D spectroscopic galaxy clustering with respect to the projected clustering. In the case of the 2D harmonic approach, we attribute this result to two main theoretical limitations of the 2D projected statistics implemented in this work according to the analysis of the official Euclid forecasts: the high shot noise and the limited redshift range of the spectroscopic sample, with respect to the photometric sample, together with the suppression of radial information from subdominant contributions such as redshift-space distortions and lensing magnification. Therefore, our analysis suggests that 2D and 3D Euclid data can be safely treated as independent, with a great saving in computational resources.