Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes

S. Casas; V. F. Cardone; D. Sapone; N. Frusciante; F. Pace; G. Parimbelli; M. Archidiacono; K. Koyama; I. Tutusaus; S. Camera; M. Martinelli; V. Pettorino; Z. Sakr; L. Lombriser; A. Silvestri; M. Pietroni; F. Vernizzi; M. Kunz; P. Ntelis; T. Kitching; A. Pourtsidou; F. Lacasa; C. Carbone; J. Garcia-Bellido; N. Aghanim; B. Altieri; A. Amara; N. Auricchio; M. Baldi; C. Bodendorf; E. Branchini; M. Brescia; J. Brinchmann; V. Capobianco; J. Carretero; M. Castellano; S. Cavuoti; A. Cimatti; R. Cledassou; G. Congedo; C. J. Conselice; L. Conversi; Y. Copin; L. Corcione; F. Courbin; H. M. Courtois; A. Da Silva; H. Degaudenzi; F. Dubath; C. A. J. Duncan; X. Dupac; S. Dusini; S. Farrens; S. Ferriol; P. Fosalba; M. Frailis; E. Franceschi; M. Fumana; S. Galeotta; B. Garilli; W. Gillard; B. Gillis; C. Giocoli; A. Grazian; F. Grupp; L. Guzzo; S. V. H. Haugan; F. Hormuth; A. Hornstrup; P. Hudelot; K. Jahnke; S. Kermiche; A. Kiessling; M. Kilbinger; H. Kurki-Suonio; S. Ligori; P. B. Lilje; I. Lloro; E. Maiorano; O. Mansutti; O. Marggraf; F. Marulli; R. Massey; E. Medinaceli; M. Meneghetti; E. Merlin; G. Meylan; M. Moresco; L. Moscardini; E. Munari; S.-M. Niemi; C. Padilla; S. Paltani; F. Pasian; K. Pedersen; W. J. Percival; S. Pires; G. Polenta; M. Poncet; L. A. Popa; F. Raison; A. Renzi; J. Rhodes; G. Riccio; E. Romelli; M. Roncarelli; E. Rossetti; R. Saglia; B. Sartoris; A. Secroun; G. Seidel; S. Serrano; C. Sirignano; G. Sirri; L. Stanco; J.-L. Starck; C. Surace; P. Tallada-Crespí; A. N. Taylor; I. Tereno; R. Toledo-Moreo; F. Torradeflot; E. A. Valentijn; L. Valenziano; T. Vassallo; Y. Wang; J. Weller; J. Zoubian; Y. Mellier; V. Scottez

doi:10.1051/0004-6361/202348713

Open Access

Issue		A&A Volume 707, March 2026


Article Number		A176
Number of page(s)		20
Section		Cosmology (including clusters of galaxies)
DOI		https://doi.org/10.1051/0004-6361/202348713
Published online		06 March 2026

A&A, 707, A176 (2026)

Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes^★

S. Casas¹^★★, V. F. Cardone²^,3, D. Sapone⁴, N. Frusciante⁵, F. Pace⁶^,7^,8, G. Parimbelli⁹^,10^,11^,12, M. Archidiacono¹³^,14, K. Koyama¹⁵, I. Tutusaus¹⁶^,17^,18^,19, S. Camera⁶^,7^,8, M. Martinelli²^,3, V. Pettorino²⁰, Z. Sakr²¹^,16^,22, L. Lombriser¹⁷, A. Silvestri²³, M. Pietroni²⁴^,25, F. Vernizzi²⁶, M. Kunz¹⁷, P. Ntelis²⁷, T. Kitching²⁸, A. Pourtsidou²⁹^,30, F. Lacasa¹⁷^,31, C. Carbone³², J. Garcia-Bellido³³, N. Aghanim³¹, B. Altieri³⁴, A. Amara¹⁵, N. Auricchio³⁵, M. Baldi³⁶^,35^,37, C. Bodendorf³⁸, E. Branchini³⁹^,40, M. Brescia⁵^,41, J. Brinchmann⁴², V. Capobianco⁸, J. Carretero⁴³^,44, M. Castellano², S. Cavuoti⁴¹^,45, A. Cimatti⁴⁶, R. Cledassou⁴⁷^,48^,†, G. Congedo²⁹, C. J. Conselice⁴⁹, L. Conversi⁵⁰^,34, Y. Copin⁵¹, L. Corcione⁸, F. Courbin⁵², H. M. Courtois⁵³, A. Da Silva⁵⁴^,55, H. Degaudenzi⁵⁶, F. Dubath⁵⁶, C. A. J. Duncan⁵⁷^,49, X. Dupac³⁴, S. Dusini⁵⁸, S. Farrens²⁰, S. Ferriol⁵¹, P. Fosalba¹⁸^,19, M. Frailis¹⁰, E. Franceschi³⁵, M. Fumana³², S. Galeotta¹⁰, B. Garilli³²^,†, W. Gillard²⁷, B. Gillis²⁹, C. Giocoli³⁵^,37, A. Grazian⁵⁹, F. Grupp³⁸^,60, L. Guzzo¹³^,61^,14, S. V. H. Haugan⁶², F. Hormuth⁶³, A. Hornstrup⁶⁴^,65, P. Hudelot⁶⁶, K. Jahnke⁶⁷, S. Kermiche²⁷, A. Kiessling⁶⁸, M. Kilbinger²⁰, H. Kurki-Suonio⁶⁹^,70, S. Ligori⁸, P. B. Lilje⁶², I. Lloro⁷¹, E. Maiorano³⁵, O. Mansutti¹⁰, O. Marggraf⁷², F. Marulli⁷³^,35^,37, R. Massey⁷⁴, E. Medinaceli³⁵, M. Meneghetti³⁵^,37, E. Merlin², G. Meylan⁵², M. Moresco⁷³^,35, L. Moscardini⁷³^,35^,37, E. Munari¹⁰, S.-M. Niemi⁷⁵, C. Padilla⁴³, S. Paltani⁵⁶, F. Pasian¹⁰, K. Pedersen⁷⁶, W. J. Percival⁷⁷^,78^,79, S. Pires²⁰, G. Polenta⁸⁰, M. Poncet⁴⁷, L. A. Popa⁸¹, F. Raison³⁸, A. Renzi⁸²^,58, J. Rhodes⁶⁸, G. Riccio⁴¹, E. Romelli¹⁰, M. Roncarelli³⁵, E. Rossetti³⁶, R. Saglia⁶⁰^,38, B. Sartoris⁶⁰^,10, A. Secroun²⁷, G. Seidel⁶⁷, S. Serrano¹⁹^,18^,83, C. Sirignano⁸²^,58, G. Sirri³⁷, L. Stanco⁵⁸, J.-L. Starck²⁰, C. Surace⁸⁴, P. Tallada-Crespí⁸⁵^,44, A. N. Taylor²⁹, I. Tereno⁵⁴^,86, R. Toledo-Moreo⁸⁷, F. Torradeflot⁴⁴^,85, E. A. Valentijn⁸⁸, L. Valenziano³⁵^,89, T. Vassallo⁶⁰^,10, Y. Wang⁹⁰, J. Weller⁶⁰^,38, J. Zoubian²⁷, Y. Mellier⁶⁶^,91^,† and V. Scottez⁹²^,93

¹ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University 52056 Aachen, Germany
² INAF-Osservatorio Astronomico di Roma Via Frascati 33 00078 Monteporzio Catone, Italy
³ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica Edificio G. Marconi 00185 Roma, Italy
⁴ Departamento de Física, FCFM, Universidad de Chile Blanco Encalada 2008 Santiago, Chile
⁵ Department of Physics “E. Pancini”, University Federico II Via Cinthia 6 80126 Napoli, Italy
⁶ Dipartimento di Fisica, Università degli Studi di Torino Via P. Giuria 1 10125 Torino, Italy
⁷ INFN-Sezione di Torino Via P. Giuria 1 10125 Torino, Italy
⁸ INAF-Osservatorio Astrofisico di Torino Via Osservatorio 20 10025 Pino Torinese (TO), Italy
⁹ Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova Via Dodecaneso 33 16146 Genova, Italy
¹⁰ INAF-Osservatorio Astronomico di Trieste Via G. B. Tiepolo 11 34143 Trieste, Italy
¹¹ SISSA, International School for Advanced Studies Via Bonomea 265 34136 Trieste TS, Italy
¹² IFPU, Institute for Fundamental Physics of the Universe Via Beirut 2 34151 Trieste, Italy
¹³ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano Via Celoria 16 20133 Milano, Italy
¹⁴ INFN-Sezione di Milano Via Celoria 16 20133 Milano, Italy
¹⁵ Institute of Cosmology and Gravitation, University of Portsmouth Portsmouth PO1 3FX, UK
¹⁶ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES 14 Av. Edouard Belin 31400 Toulouse, France
¹⁷ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics 24 quai Ernest-Ansermet CH-1211 Genève 4, Switzerland
¹⁸ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n 08193 Barcelona, Spain
¹⁹ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC 08860 Castelldefels Barcelona, Spain
²⁰ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM 91191 Gif-sur-Yvette, France
²¹ Institut für Theoretische Physik, University of Heidelberg Philosophenweg 16 69120 Heidelberg, Germany
²² Université St Joseph; Faculty of Sciences Beirut, Lebanon
²³ Institute Lorentz, Leiden University Niels Bohrweg 2 2333 CA Leiden, The Netherlands
²⁴ Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma Viale delle Scienze 7/A 43124 Parma, Italy
²⁵ INFN Gruppo Collegato di Parma Viale delle Scienze 7/A 43124 Parma, Italy
²⁶ Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France
²⁷ Aix-Marseille Université, CNRS/IN2P3, CPPM Marseille, France
²⁸ Mullard Space Science Laboratory, University College London Holmbury St Mary Dorking Surrey RH5 6NT, UK
²⁹ Institute for Astronomy, University of Edinburgh, Royal Observatory Blackford Hill Edinburgh EH9 3HJ, UK
³⁰ Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh Edinburgh EH9 3FD, UK
³¹ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale 91405 Orsay, France
³² INAF-IASF Milano Via Alfonso Corti 12 20133 Milano, Italy
³³ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco 28049 Madrid, Spain
³⁴ ESAC/ESA, Camino Bajo del Castillo, s/n. Urb. Villafranca del Castillo 28692 Villanueva de la Cañada Madrid, Spain
³⁵ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna Via Piero Gobetti 93/3 40129 Bologna, Italy
³⁶ Dipartimento di Fisica e Astronomia, Università di Bologna Via Gobetti 93/2 40129 Bologna, Italy
³⁷ INFN-Sezione di Bologna Viale Berti Pichat 6/2 40127 Bologna, Italy
³⁸ Max Planck Institute for Extraterrestrial Physics Giessenbachstr. 1 85748 Garching, Germany
³⁹ Dipartimento di Fisica, Università di Genova Via Dodecaneso 33 16146 Genova, Italy
⁴⁰ INFN-Sezione di Genova Via Dodecaneso 33 16146 Genova, Italy
⁴¹ INAF-Osservatorio Astronomico di Capodimonte Via Moiariello 16 80131 Napoli, Italy
⁴² Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP Rua das Estrelas PT4150-762 Porto, Portugal
⁴³ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB 08193 Bellaterra (Barcelona), Spain
⁴⁴ Port d’Informació Científica, Campus UAB C. Albareda s/n 08193 Bellaterra (Barcelona), Spain
⁴⁵ INFN section of Naples Via Cinthia 6 80126 Napoli, Italy
⁴⁶ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna Viale Berti Pichat 6/2 40127 Bologna, Italy
⁴⁷ Centre National d’Etudes Spatiales – Centre spatial de Toulouse 18 avenue Edouard Belin 31401 Toulouse Cedex 9, France
⁴⁸ Institut national de physique nucléaire et de physique des particules 3 rue Michel-Ange 75794 Paris Cédex 16, France
⁴⁹ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester Oxford Road Manchester M13 9PL, UK
⁵⁰ European Space Agency/ESRIN, Largo Galileo Galilei 1 00044 Frascati Roma, Italy
⁵¹ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822 Villeurbanne F-69100, France
⁵² Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny 1290 Versoix, Switzerland
⁵³ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon 4 rue Enrico Fermi 69622 Villeurbanne, France
⁵⁴ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8 Campo Grande PT1749-016 Lisboa, Portugal
⁵⁵ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande 1749-016 Lisboa, Portugal
⁵⁶ Department of Astronomy, University of Geneva ch. d’Ecogia 16 1290 Versoix, Switzerland
⁵⁷ Department of Physics, Oxford University Keble Road Oxford OX1 3RH, UK
⁵⁸ INFN-Padova Via Marzolo 8 35131 Padova, Italy
⁵⁹ INAF-Osservatorio Astronomico di Padova Via dell’Osservatorio 5 35122 Padova, Italy
⁶⁰ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München Scheinerstrasse 1 81679 München, Germany
⁶¹ INAF-Osservatorio Astronomico di Brera Via Brera 28 20122 Milano, Italy
⁶² Institute of Theoretical Astrophysics, University of Oslo P.O. Box 1029 Blindern 0315 Oslo, Norway
⁶³ von Hoerner & Sulger GmbH Schlossplatz 8 68723 Schwetzingen, Germany
⁶⁴ Technical University of Denmark Elektrovej 327 2800 Kgs. Lyngby, Denmark
⁶⁵ Cosmic Dawn Center (DAWN), Denmark
⁶⁶ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université 98 bis boulevard Arago 75014 Paris, France
⁶⁷ Max-Planck-Institut für Astronomie Königstuhl 17 69117 Heidelberg, Germany
⁶⁸ Jet Propulsion Laboratory, California Institute of Technology 4800 Oak Grove Drive Pasadena CA 91109, USA
⁶⁹ Department of Physics P.O. Box 64 00014 University of Helsinki, Finland
⁷⁰ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki Helsinki, Finland
⁷¹ NOVA optical infrared instrumentation group at ASTRON Oude Hoogeveensedijk 4 7991PD Dwingeloo, The Netherlands
⁷² Universität Bonn, Argelander-Institut für Astronomie Auf dem Hügel 71 53121 Bonn, Germany
⁷³ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna Via Piero Gobetti 93/2 40129 Bologna, Italy
⁷⁴ Department of Physics, Institute for Computational Cosmology, Durham University South Road Durham DH1 3LE, UK
⁷⁵ European Space Agency/ESTEC Keplerlaan 1 2201 AZ Noordwijk, The Netherlands
⁷⁶ Department of Physics and Astronomy, University of Aarhus Ny Munkegade 120 DK-8000 Aarhus C, Denmark
⁷⁷ Waterloo Centre for Astrophysics, University of Waterloo Waterloo Ontario N2L 3G1, Canada
⁷⁸ Department of Physics and Astronomy, University of Waterloo Waterloo Ontario N2L 3G1, Canada
⁷⁹ Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5, Canada
⁸⁰ Space Science Data Center, Italian Space Agency Via del Politecnico snc 00133 Roma, Italy
⁸¹ Institute of Space Science, Str. Atomistilor nr. 409 Măgurele Ilfov 077125, Romania
⁸² Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova Via Marzolo 8 35131 Padova, Italy
⁸³ Satlantis, University Science Park Sede Bld 48940 Leioa-Bilbao, Spain
⁸⁴ Aix-Marseille Université, CNRS, CNES, LAM Marseille, France
⁸⁵ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT) Avenida Complutense 40 28040 Madrid, Spain
⁸⁶ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa Tapada da Ajuda 1349-018 Lisboa, Portugal
⁸⁷ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras Plaza del Hospital 1 30202 Cartagena, Spain
⁸⁸ Kapteyn Astronomical Institute, University of Groningen PO Box 800 9700 AV Groningen, The Netherlands
⁸⁹ INFN-Bologna Via Irnerio 46 40126 Bologna, Italy
⁹⁰ Infrared Processing and Analysis Center, California Institute of Technology Pasadena CA 91125, USA
⁹¹ CEA Saclay, DFR/IRFU, Service d’Astrophysique Bat. 709 91191 Gif-sur-Yvette, France
⁹² Institut d’Astrophysique de Paris 98bis Boulevard Arago 75014 Paris, France
⁹³ ICL, Junia, Université Catholique de Lille, LITL 59000 Lille, France

^★★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 23 November 2023
Accepted: 5 May 2025

Abstract

We forecast the constraints that the Euclid mission will place on the Hu–Sawicki f(R) modified gravity model using galaxy clustering and weak lensing observations. Euclid’s primary probes will provide spectroscopic redshifts, photometric angular clustering, and weak lensing cosmic shear, thus allowing for precise tests of deviations from general relativity. We consider these observables to evaluate how well Euclid can constrain the extended model parameter f_R0. For a fiducial value of |f_R0| = 5 × 10⁻⁶, we find that in our baseline pessimistic setting, Euclid will constrain log₁₀|f_R0| at the 4% level with spectroscopic clustering, at 2.7% with the cross-correlation of photometric probes, and at 1.8% when combining all primary probes. This corresponds to an estimation on this model parameter of approximately |f_R0 = (5.0^+1.2_−0.9 × 10⁻⁶ at the 1σ level. We also forecast constraints for models with |f_R0| = 5 × 10⁻⁵ and |f_R0| = 5 × 10⁻⁷, finding that Euclid will distinguish these from the standard cosmological model at more than 3σ when using the full combination of primary probes. Euclid will be a powerful experiment to test modifications to gravity, provided that the theoretical systematics of the non-linear modelling are kept under control.

Key words: cosmological parameters / cosmology: observations / cosmology: theory / dark energy / large-scale structure of Universe

^★

This paper is published on behalf of the Euclid Consortium.

^†

Deceased.

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes★

Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes^★