Euclid preparation

LXXI. Simulations and nonlinearities beyond ΛCDM. 3. Constraints on f(R) models from the photometric primary probes

¹ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
² Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁴ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
⁵ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁶ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁷ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
⁸ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁹ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹⁰ Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
¹¹ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
¹² INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
¹³ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
¹⁴ Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, UK
¹⁵ Institut universitaire de France (IUF), 1 rue Descartes, 75231 Paris CEDEX 05, France
¹⁶ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
¹⁷ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
¹⁸ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
¹⁹ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway
²⁰ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
²¹ Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
²² Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
²³ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
²⁴ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
²⁵ Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n Cerdanyola del Vallés, 08193 Barcelona, Spain
²⁶ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
²⁷ Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
²⁸ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
²⁹ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
³⁰ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
³¹ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
³² INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
³³ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
³⁴ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
³⁵ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
³⁶ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
³⁷ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
³⁸ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
³⁹ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
⁴⁰ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴¹ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
⁴² Faculdade de Ciências da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal
⁴³ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁴⁴ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁵ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
⁴⁶ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
⁴⁷ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁴⁸ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
⁴⁹ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
⁵⁰ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
⁵¹ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵² Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
⁵³ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁵⁴ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁵⁵ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
⁵⁶ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁵⁷ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁵⁸ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁵⁹ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁶⁰ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁶¹ Université Paris-Saclay, CNRS, Institut d’astrophysique Spatiale, 91405 Orsay, France
⁶² INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁶³ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁶⁴ INAF-Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁶⁵ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁶⁶ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁶⁷ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁶⁸ FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231 Las Rozas de Madrid, Spain
⁶⁹ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁷⁰ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁷¹ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁷² Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
⁷³ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁷⁴ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁷⁵ Cosmic Dawn Center (DAWN), Copenhagen, Denmark
⁷⁶ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
⁷⁷ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁷⁸ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁷⁹ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁸⁰ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁸¹ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁸² Department of Physics, P.O. Box 64 00014 University of Helsinki, Helsinki, Finland
⁸³ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁸⁴ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands
⁸⁵ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁸⁶ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁸⁷ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
⁸⁸ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Via Piero Gobetti 93/2, 40129 Bologna, Italy
⁸⁹ Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
⁹⁰ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁹¹ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁹² Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁹³ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
⁹⁴ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁹⁵ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁹⁶ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁹⁷ Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁹⁸ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁹⁹ Space Science Data Center, Italian Space Agency, Via del Politecnico snc, 00133 Roma, Italy
¹⁰⁰ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 Avenue Edouard Belin, 31401 Toulouse Cedex 9, France
¹⁰¹ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
¹⁰² Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
¹⁰³ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada, 2008 Santiago, Chile
¹⁰⁴ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
¹⁰⁵ Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
¹⁰⁶ Department of Physics, Royal Holloway, University of London, London TW20 0EX, UK
¹⁰⁷ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
¹⁰⁸ Cosmic Dawn Center (DAWN), Copenhagen, Denmark
¹⁰⁹ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹¹⁰ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹¹¹ Kapteyn Astronomical Institute, University of Groningen, PO Box 800 9700 AV Groningen, The Netherlands
¹¹² Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹¹³ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
¹¹⁴ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹¹⁵ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus (Aosta Valley), Italy
¹¹⁶ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹¹⁷ School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, UK
¹¹⁸ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹¹⁹ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
¹²⁰ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹²¹ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
¹²² Departamento de Física Fundamental. Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain
¹²³ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹²⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹²⁵ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹²⁶ Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
¹²⁷ Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany
¹²⁸ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA
¹²⁹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
¹³⁰ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹³¹ Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary’s University, 923 Robie Street, Halifax Nova Scotia B3H 3C3, Canada
¹³² Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹³³ Instituto de Astrofísica de Canarias (IAC); Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
¹³⁴ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹³⁵ CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France
¹³⁶ Department of Computer Science, Aalto University, PO Box 15400 Espoo FI-00 076, Finland
¹³⁷ Instituto de Astrofísica de Canarias, c/ Via Lactea s/n, La Laguna 38200, Spain. Departamento de Astrofísica de la Universidad de La Laguna, Avda. Francisco Sanchez, La Laguna 38200, Spain
¹³⁸ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France
¹³⁹ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Finland
¹⁴⁰ Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁴¹ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹⁴² Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹⁴³ School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
¹⁴⁴ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
¹⁴⁵ ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil
¹⁴⁶ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁴⁷ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm SE-106 91, Sweden
¹⁴⁸ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
¹⁴⁹ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁵⁰ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹⁵¹ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁵² HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁵³ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹⁵⁴ Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515 751 20 Uppsala, Sweden
¹⁵⁵ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁵⁶ Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA
¹⁵⁷ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA

^⋆ Corresponding author: kazuya.koyama@port.ac.uk

Received: 9 September 2024
Accepted: 13 March 2025

Abstract

We study the constraint on f(R) gravity that can be obtained by photometric primary probes of the Euclid mission. Our focus is the dependence of the constraint on the theoretical modelling of the nonlinear matter power spectrum. In the Hu–Sawicki f(R) gravity model, we consider four different predictions for the ratio between the power spectrum in f(R) and that in Λ cold dark matter (ΛCDM): a fitting formula, the halo model reaction approach, ReACT, and two emulators based on dark matter only N-body simulations, FORGE and e-Mantis. These predictions are added to the MontePython implementation to predict the angular power spectra for weak lensing (WL), photometric galaxy clustering, and their cross-correlation. By running Markov chain Monte Carlo, we compare constraints on parameters and investigate the bias of the recovered f(R) parameter if the data are created by a different model. For the pessimistic setting of WL, one-dimensional bias for the f(R) parameter, log₁₀|f_R0|, is found to be 0.5σ when FORGE is used to create the synthetic data with log₁₀|f_R0| = −5.301 and fitted by e-Mantis. The impact of baryonic physics on WL is studied by using a baryonification emulator, BCemu. For the optimistic setting, the f(R) parameter and two main baryonic parameters are well constrained despite the degeneracies among these parameters. However, the difference in the nonlinear dark matter prediction can be compensated for the adjustment of baryonic parameters, and the one-dimensional marginalised constraint on log₁₀|f_R0| is biased. This bias can be avoided in the pessimistic setting at the expense of weaker constraints. For the pessimistic setting, using the ΛCDM synthetic data for WL, we obtain the prior-independent upper limit of log₁₀|f_R0| < −5.6. Finally, we implement a method to include theoretical errors to avoid the bias due to inaccuracies in the nonlinear matter power spectrum prediction.