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

TL;DR

This work conducts a comprehensive model comparison for the redshift-space two-point galaxy statistics relevant to Euclid, focusing on even multipoles of the 2-point correlation function. By testing EFT, velocity-difference generators, and LPT-based models (including CLPT and CLEFT) against Flagship 1 halos across $z o 0.9$–$1.8$, it evaluates template-fitting and full-shape analyses to identify models capable of delivering Euclid-level accuracy. The study finds that nonperturbative treatments like VDG$_{ ext∞}$ and CLEFT are essential to reach small scales ($s_{ m min} o 20~h^{-1}{ m Mpc}$) at low redshift, while at higher redshift simpler models (e.g., CLPT) can suffice for high-figure-of-merit constraints. The results establish baseline, robust modelling options for configuration-space Euclid analyses and demonstrate the role of emulators in enabling efficient full-shape inference, setting the stage for incorporating observational systematics in future work.

Abstract

The Euclid satellite will measure spectroscopic redshifts for tens of millions of emission-line galaxies. In the context of Stage-IV surveys, the 3-dimensional clustering of galaxies plays a key role in providing cosmological constraints. In this paper, we conduct a model comparison for the multipole moments of the galaxy 2-point correlation function (2PCF) in redshift space. We test state-of-the-art models, in particular the effective field theory of large-scale structure (EFT), one based on the velocity difference generating function (VDG$_{\infty}$), and different variants of Lagrangian perturbation theory (LPT) models, such as convolutional LPT (CLPT) and its effective-field-theory extension (CLEFT). We analyse the first three even multipoles of the 2PCF in the Flagship 1 simulation, which consists of four snapshots at $z\in\{0.9,1.2,1.5,1.8\}$. We study both template-fitting and full-shape approaches and find that with the template-fitting approach, only the VDG$_{\infty}$ model is able to reach a minimum fitting scale of $s_{\rm min}=20\,h^{-1}\,{\rm Mpc}$ at $z=0.9$ without biasing the recovered parameters. Indeed, the EFT model becomes inaccurate already at $s_{\rm min}=30\,h^{-1}\,{\rm Mpc}$. Conversely, in the full-shape analysis, the CLEFT and VDG$_{\infty}$ models perform similarly well, but only the CLEFT model can reach $s_{\rm min}=20\,h^{-1}\,{\rm Mpc}$ while the VDG$_{\infty}$ model is unbiased down to $s_{\rm min}=25\,h^{-1}\,{\rm Mpc}$ at the lowest redshift. Overall, in order to achieve the accuracy required by Euclid, non-perturbative modelling such as in the VDG$_{\infty}$ or CLEFT models should be considered. At $z=1.8$, the CLPT model is sufficient to describe the data with 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.

Figures (13)

• Figure 1: Performance metrics for the fixed-cosmology case of the , , , and model as a function of the minimum fitting scale $s_{\mathrm{min}}$. The shaded regions in the panels displaying the $\chi^2_{\rm red}$ values refer to the standard deviation and twice the standard deviation of the $\chi^2_{\rm red}$ distribution with the model degrees of freedom fixed to seven () as a conservative choice. In the panels, the two shaded regions denote the 68-th and 95-th percentiles as described in Sect. \ref{['sec:performance_metrics']}.
• Figure 2: Percent relative difference between the recovered parameters of the template-fitting approach with respect to their fiducial values. Each of the models under consideration (, , , ) is represented by three data points for every redshift, corresponding to the recovered values using a progressively smaller value of $s_{\mathrm{min}} \in \{40, 30,20\}\, h^{-1} \, {\rm Mpc}$ from left to right. The grey shaded area marks an accuracy of 1% across all parameters.
• Figure 3: Performance metrics of the , , , and model for the full-shape analysis as a function of the minimum fitting scale $s_{\mathrm{min}}$. The shaded regions in the panels displaying the $\chi^2_{\rm red}$ values refer to the standard deviation and twice the standard deviation of the $\chi^2_{\rm red}$ distribution with the model degrees of freedom fixed to six () as a conservative choice. For the , the two shaded regions denote the 68-th and 95-th percentiles as described in Sect. \ref{['sec:performance_metrics']}.
• Figure 4: Same as in Fig. \ref{['fig:fixed_cosmo_params']}, but for the full-shape analysis constraining the cosmological parameters $h$, $A_\mathrm{s}$, and $\omega_\text{c}$.
• Figure 5: Top: Legendre multipoles of the as measured from the Flagship 1 snapshot at $z=0.9$ (black errorbars) against the different model predictions evaluated with the mean values of the corresponding posterior distribution at $s_{\mathrm{min}}=20\, h^{-1} \, {\rm Mpc}$. Bottom: Relative difference between the data points and the different models in units of the diagonal of the covariance matrix (its square root). The grey shaded region refers to a difference of $1\sigma$.