Euclid preparation. Full-shape modelling of 2-point and 3-point correlation functions in real space
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.
Cite
@article{arxiv.2506.22257,
title = {Euclid preparation. Full-shape modelling of 2-point and 3-point correlation functions in real space},
author = {Euclid Collaboration and M. Guidi and A. Veropalumbo and A. Pugno and M. Moresco and E. Sefusatti and C. Porciani and E. Branchini and M. -A. Breton and B. Camacho Quevedo and M. Crocce and S. de la Torre and V. Desjacques and A. Eggemeier and A. Farina and M. Kärcher and D. Linde and M. Marinucci and A. Moradinezhad Dizgah and C. Moretti and K. Pardede and A. Pezzotta and E. Sarpa and A. Amara and S. Andreon and N. Auricchio and C. Baccigalupi and D. Bagot and M. Baldi and S. Bardelli and P. Battaglia and A. Biviano and M. Brescia and S. Camera and G. Cañas-Herrera and V. Capobianco and C. Carbone and V. F. Cardone and J. Carretero and M. Castellano and G. Castignani and S. Cavuoti and K. C. Chambers and A. Cimatti and C. Colodro-Conde and G. Congedo and L. Conversi and Y. Copin and F. Courbin and H. M. Courtois and A. Da Silva and H. Degaudenzi and G. De Lucia and H. Dole and M. Douspis and F. Dubath and X. Dupac and S. Dusini and S. Escoffier and M. Farina and R. Farinelli and F. Faustini and S. Ferriol and F. Finelli and P. Fosalba and S. Fotopoulou and M. Frailis and E. Franceschi and M. Fumana and S. Galeotta and B. Gillis and C. Giocoli and J. Gracia-Carpio and A. Grazian and F. Grupp and L. Guzzo and S. V. H. Haugan and W. Holmes and F. Hormuth and A. Hornstrup and K. Jahnke and M. Jhabvala and B. Joachimi and E. Keihänen and S. Kermiche and A. Kiessling and B. Kubik and M. Kümmel and M. Kunz and H. Kurki-Suonio and A. M. C. Le Brun and S. Ligori and P. B. Lilje and V. Lindholm and I. Lloro and G. Mainetti and D. Maino and E. Maiorano and O. Mansutti and S. Marcin and O. Marggraf and K. Markovic and M. Martinelli and N. Martinet and F. Marulli and R. Massey and E. Medinaceli and S. Mei and M. Melchior and Y. Mellier and M. Meneghetti and E. Merlin and G. Meylan and A. Mora and B. Morin and L. Moscardini and E. Munari and C. Neissner and S. -M. Niemi and C. Padilla and S. Paltani and F. Pasian and K. Pedersen and W. J. Percival and V. Pettorino and S. Pires and G. Polenta and M. Poncet and L. A. Popa and F. Raison and R. Rebolo and A. Renzi and J. Rhodes and G. Riccio and E. Romelli and M. Roncarelli and R. Saglia and Z. Sakr and A. G. Sánchez and D. Sapone and B. Sartoris and J. A. Schewtschenko and P. Schneider and T. Schrabback and M. Scodeggio and A. Secroun and G. Seidel and M. Seiffert and S. Serrano and P. Simon and C. Sirignano and G. Sirri and A. Spurio Mancini and L. Stanco and J. Steinwagner and P. Tallada-Crespí and D. Tavagnacco and A. N. Taylor and I. Tereno and N. Tessore and S. Toft and R. Toledo-Moreo and F. Torradeflot and A. Tsyganov and I. Tutusaus and L. Valenziano and J. Valiviita and T. Vassallo and G. Verdoes Kleijn and Y. Wang and J. Weller and G. Zamorani and F. M. Zerbi and E. Zucca and V. Allevato and M. Ballardini and M. Bolzonella and E. Bozzo and C. Burigana and R. Cabanac and M. Calabrese and A. Cappi and D. Di Ferdinando and J. A. Escartin Vigo and L. Gabarra and J. Martín-Fleitas and S. Matthew and M. Maturi and N. Mauri and R. B. Metcalf and A. A. Nucita and M. Pöntinen and I. Risso and V. Scottez and M. Sereno and M. Tenti and M. Viel and M. Wiesmann and Y. Akrami and I. T. Andika and S. Anselmi and M. Archidiacono and F. Atrio-Barandela and A. Balaguera-Antolinez and D. Bertacca and M. Bethermin and L. Blot and H. Böhringer and S. Borgani and M. L. Brown and S. Bruton and A. Calabro and F. Caro and C. S. Carvalho and T. Castro and F. Cogato and S. Conseil and S. Contarini and A. R. Cooray and O. Cucciati and S. Davini and F. De Paolis and G. Desprez and A. Díaz-Sánchez and J. J. Diaz and S. Di Domizio and J. M. Diego and P. Dimauro and A. Enia and Y. Fang and A. G. Ferrari and P. G. Ferreira and A. Finoguenov and A. Franco and K. Ganga and J. García-Bellido and T. Gasparetto and V. Gautard and E. Gaztanaga and F. Giacomini and F. Gianotti and G. Gozaliasl and C. M. Gutierrez and C. Hernández-Monteagudo and H. Hildebrandt and J. Hjorth and S. Joudaki and J. J. E. Kajava and Y. Kang and V. Kansal and D. Karagiannis and K. Kiiveri and C. C. Kirkpatrick and S. Kruk and M. Lattanzi and L. Legrand and M. Lembo and F. Lepori and G. Leroy and G. F. Lesci and J. Lesgourgues and L. Leuzzi and T. I. Liaudat and A. Loureiro and J. Macias-Perez and G. Maggio and M. Magliocchetti and F. Mannucci and R. Maoli and C. J. A. P. Martins and L. Maurin and M. Miluzio and P. Monaco and G. Morgante and S. Nadathur and K. Naidoo and A. Navarro-Alsina and S. Nesseris and L. Pagano and F. Passalacqua and K. Paterson and L. Patrizii and A. Pisani and D. Potter and S. Quai and M. Radovich and P. Reimberg and P. -F. Rocci and G. Rodighiero and S. Sacquegna and M. Sahlén and D. B. Sanders and A. Schneider and D. Sciotti and E. Sellentin and L. C. Smith and J. G. Sorce and K. Tanidis and C. Tao and G. Testera and R. Teyssier and S. Tosi and A. Troja and M. Tucci and C. Valieri and A. Venhola and D. Vergani and F. Vernizzi and G. Verza and P. Vielzeuf and N. A. Walton},
journal= {arXiv preprint arXiv:2506.22257},
year = {2026}
}
Comments
21 pages, 11 figures