Euclid preparation. CI. Galaxy 2-point correlation function modelling in redshift space

The Euclid satellite will measure spectroscopic redshifts for tens of millions of emission-line galaxies, allowing for one of the most precise tests of the cosmological model. In the context of Stage-IV surveys such as Euclid, the 3D clustering of galaxies plays a key role, providing both geometrical and dynamical cosmological constraints. In this paper, we conduct a comprehensive model comparison campaign for the multipole moments of the galaxy 2-point correlation function (2PCF) in redshift space. We tested state-of-the-art models, in particular the effective field theory of large-scale structure (EFT), a model based on the velocity difference generating function (VDG_∞), and variants of the Lagrangian perturbation theory (LPT), namely convolutional Lagrangian perturbation theory (CLPT) and convolutional Lagrangian effective field theory (CLEFT). We analysed the first three even multipole moments of the 2PCF in the simulation of emission-line galaxies, which consists of four snapshots at z∈ 1. 2, 1. 5, 1. 8 covering the redshift range of the Euclid spectroscopic sample. We studied template-fitting and full-shape approaches and compared the different models in terms of three performance metrics: reduced ̧hi², a figure of merit, and a figure of bias. We find that with the template-fitting approach, only the VDG_∞ model is able to reach a minimum fitting scale of smin=20 at z=0. 9 without biasing the recovered parameters. Indeed, the EFT model becomes inaccurate already at smin=30 Conversely, in the full-shape analysis, the CLEFT and VDG_∞ models perform similarly well, but only the CLEFT model can reach smin=20 while the VDG_∞ model is unbiased down to smin=25 at the lowest redshift. Overall, in order to achieve the accuracy required by Euclid, non-perturbative modelling, such as in the VDG_∞ or CLEFT models, should be considered. At the highest redshift probed by Euclid, the CLPT model is sufficient to describe the data with a high figure of merit. This comparison selects baseline models that perform best in ideal conditions and sets the stage for an optimal analysis of Euclid data in configuration space.