Euclid: Modelling observational effects in cluster counts and cluster clustering^★

¹ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
² Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
³ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
⁴ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
⁵ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
⁶ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
⁷ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
⁸ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁹ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
¹⁰ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
¹¹ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
¹² ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
¹³ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
¹⁴ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
¹⁵ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹⁶ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
¹⁷ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
¹⁸ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹⁹ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²⁰ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
²¹ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
²² Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
²³ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁴ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
²⁵ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands
²⁶ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA, Leiden, The Netherlands
²⁷ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC, Leiden, The Netherlands
²⁸ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
²⁹ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
³⁰ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
³¹ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³² INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
³³ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
³⁴ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
³⁵ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁶ Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
³⁷ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³⁸ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
³⁹ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
⁴⁰ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁴¹ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁴² UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁴³ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁴⁴ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁴⁵ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁴⁶ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁴⁷ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁴⁸ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
⁴⁹ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁵⁰ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁵¹ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁵² Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁵³ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵⁴ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁵⁵ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁵⁶ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁵⁷ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁵⁸ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁵⁹ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁶⁰ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway
⁶¹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁶² Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁶³ Technical University of Denmark, Elektrovej 327, 2800 Kgs., Lyngby, Denmark
⁶⁴ Cosmic Dawn Center (DAWN), Denmark
⁶⁵ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁶⁶ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁶⁷ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁶⁸ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁶⁹ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁷⁰ Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland
⁷¹ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁷² Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁷³ SKAO, Jodrell Bank, Lower Withington, Macclesfield SK11 9FT, United Kingdom
⁷⁴ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁷⁵ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷⁶ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
⁷⁷ Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
⁷⁸ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁷⁹ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3 Berkeley, USA
⁸⁰ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁸¹ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁸² Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁸³ University Observatory, LMU Faculty of Physics, Scheinerstrasse 1, 81679 Munich, Germany
⁸⁴ Telespazio UK S.L. for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
⁸⁵ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁸⁶ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁸⁷ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁸⁸ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁸⁹ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov, 077125, Romania
⁹⁰ Consejo Superior de Investigaciones Cientificas, Calle Serrano 117, 28006 Madrid, Spain
⁹¹ Universidad de La Laguna, Departamento de Astrofísica, 38206 La Laguna, Tenerife, Spain
⁹² Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁹³ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁹⁴ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁹⁵ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁹⁶ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁹⁷ Satlantis, University Science Park, Sede Bld, 48940 Leioa-Bilbao, Spain
⁹⁸ Department of Physics, Royal Holloway, University of London, Surrey TW20 0EX, UK
⁹⁹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
¹⁰⁰ Cosmic Dawn Center (DAWN)
¹⁰¹ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁰² Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹⁰³ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands
¹⁰⁴ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
¹⁰⁵ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹⁰⁶ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹⁰⁷ Zentrum für Astronomie, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
¹⁰⁸ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France

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Received: 15 October 2025
Accepted: 23 March 2026

Abstract

This study explores the impact of observational and modelling systematic effects on cluster number counts and cluster clustering and provides model prescriptions for their joint analysis in the context of the Euclid survey. Using 1000 Euclid-like cluster catalogues, we investigated the effect of systematic uncertainties on cluster summary statistics and their auto- and cross-covariance, and performed a likelihood analysis to evaluate their impact on cosmological constraints, with a focus on the matter density parameter (Ω_m) and on the power spectrum amplitude (σ₈). Combining cluster clustering with number counts significantly improves cosmological constraints, with the figure of merit increasing by over 300% compared to number counts alone. We confirm that the two probes are uncorrelated, and the cosmological constraints derived from their combination are almost insensitive to the cosmology dependence of the covariance. We find that photometric redshift uncertainties broaden cosmological posteriors by 20–30%, while secondary effects such as redshift-space distortions (RSDs) have a smaller impact on the posteriors – 5% for clustering alone, 10% when combining probes – but can significantly bias the constraints if neglected. We show that clustering data below 60 h⁻¹ Mpc provides additional constraining power, while scales larger than the acoustic oscillation scale add almost no information on Ω_m and σ₈ parameters. The RSDs and photo-z uncertainties also influence the number count covariance, with a significant impact of about 15–20% on the parameter constraints.