Euclid preparation. Full-shape modelling of 2-point and 3-point correlation functions in real space

TL;DR

This paper evaluates the accuracy of perturbative models for 2-point and 3-point galaxy correlation functions in real space, develops an emulator for efficient analysis, and performs the first joint full-shape analysis to constrain cosmological parameters relevant for Euclid.

Contribution

It introduces a novel emulator for joint analysis of 2PCF and 3PCF, extending the model to include multiple cosmological parameters, and validates the model's performance down to 30 Mpc/h.

Findings

Overall agreement with data down to 20 Mpc/h

First joint full-shape analysis of 2PCF and 3PCF

Optimal scale cut of 30 Mpc/h for 3PCF

Abstract

We investigate the accuracy and range of validity of the perturbative model for the 2-point (2PCF) and 3-point (3PCF) correlation functions in real space in view of the forthcoming analysis of the Euclid mission spectroscopic sample. We take advantage of clustering measurements from four snapshots of the Flagship I N-body simulations at z = {0.9, 1.2, 1.5, 1.8}, which mimic the expected galaxy population in the ideal case of absence of observational effects such as purity and completeness. For the 3PCF we consider all available triangle configurations given a minimal separation. First, we assess the model performance by fixing the cosmological parameters and evaluating the goodness-of-fit provided by the perturbative bias expansion in the joint analysis of the two statistics, finding overall agreement with the data down to separations of 20 Mpc/h. Subsequently, we build on the state-of-the-art and extend the analysis to include the dependence on three cosmological parameters: the amplitude of scalar perturbations As, the matter density {\omega}cdm and the Hubble parameter h. To achieve this goal, we develop an emulator capable of generating fast and robust modelling predictions for the two summary statistics, allowing efficient sampling of the joint likelihood function. We therefore present the first joint full-shape analysis of the real-space 2PCF and 3PCF, testing the consistency and constraining power of the perturbative model across both probes, and assessing its performance in a combined likelihood framework. We explore possible systematic uncertainties induced by the perturbative model at small scales finding an optimal scale cut of rmin = 30 Mpc/h for the 3PCF, when imposing an additional limitation on nearly isosceles triangular configurations included in the data vector. This work is part of a Euclid Preparation series validating theoretical models for galaxy clustering.