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

The Euclid satellite will measure spectroscopic redshifts for tens of millions of galaxies, allowing for one of the most precise tests of the cosmological model. In the context of Stage-IV surveys such as Euclid, the 3-dimensional clustering of galaxies plays a key role in both providinggeometrical and dynamical constraints. In this paper, we conduct a comprehensive model-comparison campaign for the galaxy 2-point correlation function (2PCF) multipole moments in redshift space. We test state-of-the-art models, in particular the effective field theory of large-scalestructure (EFT), one based on the velocity difference generating function (VDG∞), and different flavours of Lagrangian perturbation theory (LPT)models, such as convolutional Lagrangian perturbation theory (CLPT) and convolutional Lagrangian effective field theory (CLEFT). We analysethe first three even multipole moments of the 2PCF in the Flagship 1 simulation of emission-line galaxies, which consists of four snapshots atz ∈ {0.9, 1.2, 1.5, 1.8} covering the redshift range of the Euclid spectroscopic sample. We study both template-fitting and full-shape approaches andcompare the different models in terms of three performance metrics: reduced chi-squared, a figure of merit, and a figure of bias. We find that withthe template-fitting approach, only the VDG∞ model is able to reach a minimum fitting scale of smin = 20 h−1 Mpc without biasing the recoveredparameters. On the contrary, the EFT model becomes inaccurate already at smin = 30 h−1 Mpc. Conversely, in the full-shape analysis, the CLEFTand VDG∞ models perform similarly well, but only the CLEFT model can reach smin = 20 h−1 Mpc while the VDG∞ model is unbiased down tosmin = 25 h−1 Mpc. Overall, in order to achieve the exquisite accuracy required by Euclid, non-perturbative modelling such as in the VDG∞ orCLEFT models should be considered. Even though, at the highest redshift probed by Euclid, the CLPT model is sufficient to describe the datawith high figure of merit. This comparison sets the stage for the selection of an optimal model to be used for the clustering analysis of Euclid datain configuration space.Key words. Cosmology: large-scale structure of Universe, theory, cosmological parameters