Euclid preparation

LXXXV. Toward a DR1 application of higher-order weak lensing statistics

¹ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
² Scuola Superiore Meridionale, Via Mezzocannone 4, 80138 Napoli, Italy
³ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴ School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, Newcastle-upon-Tyne NE1 7RU, UK
⁵ Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
⁶ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁷ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁸ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁹ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁰ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
¹¹ INFN-Sezione di Roma,, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica Edificio G. Marconi, 00185 Roma, Italy
¹² Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1 Roma, Italy
¹³ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹⁴ Université Paris-Saclay, CEA, Département d’Électronique des Détecteurs et d’Informatique pour la Physique, 91191 Gif-sur-Yvette, France
¹⁵ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
¹⁶ Mathematical Institute, University of Leiden, Einsteinweg 55, 2333 CA Leiden, The Netherlands
¹⁷ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
¹⁸ Center for Cosmology and AstroParticle Physics, The Ohio State University, 191 West Woodruff Avenue Columbus, OH 43210, USA
¹⁹ Department of Physics, The Ohio State University, Columbus, OH 43210, USA
²⁰ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
²¹ Department of Astronomy and Astrophysics, University of California,, Santa Cruz 1156 High Street Santa Cruz, CA 95064, USA
²² Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
²³ CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France
²⁴ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
²⁵ Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Avenida Gran Bretana 1111 Valparaíso, Chile
²⁶ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
²⁷ Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France
²⁸ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
²⁹ Institutes of Computer Science and Astrophysics, Foundation for Research and Technology – Hellas (FORTH), N. Plastira 100, Voutes GR-70013 Heraklion, Greece
³⁰ University of Crete, Department of Physics, GR-70013 Heraklion, Greece
³¹ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
³² Institute for Advanced Study, 1 Einstein Dr., NJ 08540, USA
³³ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
³⁴ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa,, Edifício C8 Campo Grande, PT1749-016 Lisboa, Portugal
³⁵ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
³⁶ ESAC/ESA, Camino Bajo del Castillo,, s/n. Urb. Villafranca del Castillo, 28692, Villanueva de la Cañada Madrid, Spain
³⁷ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
³⁸ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
³⁹ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
⁴⁰ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
⁴¹ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
⁴² Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁴³ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁴⁴ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
⁴⁵ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
⁴⁶ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁴⁷ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁴⁸ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
⁴⁹ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁵⁰ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
⁵¹ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁵² Port d’Informació Científica,, Campus UAB C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
⁵³ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive Honolulu, HI 96822, USA
⁵⁴ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵⁵ Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
⁵⁶ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill Edinburgh, EH9 3HJ, UK
⁵⁷ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044, Frascati Roma, Italy
⁵⁸ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France
⁵⁹ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁶⁰ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁶¹ Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n Cerdanyola del Vallés, 08193 Barcelona, Spain
⁶² UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁶³ Mullard Space Science Laboratory, University College London, Holmbury St Mary Dorking, Surrey, RH5 6NT, UK
⁶⁴ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁶⁵ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁶⁶ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
⁶⁷ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁶⁸ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁶⁹ INAF-Istituto di Astrofisica e Planetologia Spaziali,, Via del Fosso del Cavaliere 100, 00100 Roma, Italy
⁷⁰ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁷¹ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁷² University Observatory, LMU Faculty of Physics, Scheinerstrasse 1, 81679 Munich, Germany
⁷³ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁷⁴ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁷⁵ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway
⁷⁶ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive Pasadena, CA 91109, USA
⁷⁷ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁷⁸ Technical University of Denmark,, Elektrovej 327 2800 Kgs. Lyngby, Denmark
⁷⁹ Cosmic Dawn Center (DAWN),, Denmark
⁸⁰ Max-Planck-Institut für Astronomie,, Königstuhl 17, 69117 Heidelberg, Germany
⁸¹ NASA Goddard Space Flight Center, Greenbelt MD 20771, USA
⁸² Department of Physics and Astronomy, University College London, Gower Street London, WC1E 6BT, UK
⁸³ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁸⁴ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁸⁵ Department of Physics, P.O. Box 64 University of Helsinki, 00014 Helsinki, Finland
⁸⁶ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁸⁷ Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁸⁸ SKAO, Jodrell Bank, Lower Withington, Macclesfield, SK11 9FT, UK
⁸⁹ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁹⁰ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁹¹ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁹² Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Via Piero Gobetti 93/2, 40129 Bologna, Italy
⁹³ Department of Physics, Institute for Computational Cosmology, Durham University, South Road Durham, DH1 3LE, UK
⁹⁴ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁹⁵ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3 Berkeley, USA
⁹⁶ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁹⁷ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁹⁸ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁹⁹ 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
¹⁰⁰ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
¹⁰¹ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
¹⁰² Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
¹⁰³ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
¹⁰⁴ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
¹⁰⁵ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
¹⁰⁶ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
¹⁰⁷ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
¹⁰⁸ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008 Santiago, Chile
¹⁰⁹ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
¹¹⁰ Satlantis, University Science Park, Sede Bld 48940 Leioa-Bilbao, Spain
¹¹¹ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans,, s/n 08193 Barcelona, Spain
¹¹² Department of Physics, Royal Holloway, University of London, Surrey, TW20 0EX, UK
¹¹³ Cosmic Dawn Center (DAWN),
¹¹⁴ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹¹⁵ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹¹⁶ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
¹¹⁷ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹⁸ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹⁹ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹²⁰ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus (Aosta Valley), Italy
¹²¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
¹²² Department of Physics, Oxford University, Keble Road, Oxford, OX1 3RH, UK
¹²³ Aurora Technology for European Space Agency (ESA),, Camino bajo del Castillo, s/n Urbanizacion Villafranca del Castillo, Villanueva de la Cañada 28692 Madrid, Spain
¹²⁴ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹²⁵ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2 Bologna, Italy
¹²⁶ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹²⁷ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue Cleveland, OH 44106, USA
¹²⁸ Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Str. 1, 85748 Garching, Germany
¹²⁹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
¹³⁰ Donostia International Physics Center (DIPC),, Paseo Manuel de Lardizabal 4, 20018, Donostia-San Sebastián Guipuzkoa, Spain
¹³¹ IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
¹³² Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
¹³³ Departamento de Física Fundamental. Universidad de Salamanca, Plaza de la Merced s/n. 37008, Salamanca, Spain
¹³⁴ IRFU, CEA, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France
¹³⁵ Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
¹³⁶ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹³⁷ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹³⁸ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road Manchester, M13 9PL, UK
¹³⁹ California Institute of Technology, 1200 E California Blvd Pasadena, CA 91125, USA
¹⁴⁰ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹⁴¹ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
¹⁴² Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹⁴³ Instituto de Física de Cantabria, Edificio Juan Jordá, Avenida de los Castros, 39005 Santander, Spain
¹⁴⁴ INFN, Sezione di Lecce,, Via per Arnesano CP-193, 73100 Lecce, Italy
¹⁴⁵ Department of Mathematics and Physics E. De Giorgi, University of Salento,, Via per Arnesano CP-I93, 73100 Lecce, Italy
¹⁴⁶ INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100 Lecce, Italy
¹⁴⁷ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK
¹⁴⁸ Department of Computer Science, Aalto University, PO Box 15400 Espoo, FI-00 076, Finland
¹⁴⁹ 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
¹⁵⁰ Caltech/IPAC, 1200 E. California Blvd. Pasadena, CA 91125, USA
¹⁵¹ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹⁵² Department of Physics and Astronomy,, Vesilinnantie 5 University of Turku, 20014 Turku, Finland
¹⁵³ Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁵⁴ Department of Physics and Astronomy, University of the Western Cape, Bellville Cape Town 7535, South Africa
¹⁵⁵ DAMTP, Centre for Mathematical Sciences, Wilberforce Road Cambridge, CB3 0WA, UK
¹⁵⁶ Kavli Institute for Cosmology Cambridge, Madingley Road Cambridge, CB3 0HA, UK
¹⁵⁷ Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹⁵⁸ Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road Durham, DH1 3LE, UK
¹⁵⁹ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
¹⁶⁰ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3,, 53 Avenue des Martyrs, 38000 Grenoble, France
¹⁶¹ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁶² Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁶³ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
¹⁶⁴ HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁶⁵ INAF – Osservatorio Astronomico d’Abruzzo, Via Maggini, 64100 Teramo, Italy
¹⁶⁶ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 37 Uppsala, Sweden
¹⁶⁷ Institute of Astronomy, University of Cambridge, Madingley Road Cambridge, CB3 0HA, UK
¹⁶⁸ Department of Astrophysical Sciences,, Peyton Hall Princeton University Princeton, NJ 08544, USA
¹⁶⁹ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA

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Received: 6 October 2025
Accepted: 15 December 2025

Abstract

This is the second paper in the HOWLS (higher-order weak lensing statistics) series exploring the usage of non-Gaussian statistics for cosmology inference within Euclid. With respect to our first paper, we develop a full tomographic analysis based on realistic photometric redshifts that allows us to derive Fisher forecasts in the (σ₈, w₀) plane for a Euclid-like data release 1 (DR1) setup. We find that the five higher-order statistics (HOS) that satisfy the Gaussian likelihood assumption of the Fisher formalism (one-point probability distribution function, ℓ1-norm, peak counts, Minkowski functionals, and Betti numbers) each outperform the shear two-point correlation functions by a factor of 2.5 on the w₀ forecasts, with only marginal improvement when used in combination with two-point estimators, suggesting that every HOS is able to retrieve both the non-Gaussian and Gaussian information of the matter density field. The similar performance of the different estimators is explained by a homogeneous use of multi-scale and tomographic information, optimized to lower computational costs. These results hold for the three mass mapping techniques of the Euclid pipeline, aperture mass, Kaiser–Squires, and Kaiser–Squires plus, and they are unaffected by the application of realistic star masks. Finally, we explored the use of HOS with the Bernardeau–Nishimichi–Taruya (BNT) nulling scheme approach, finding promising results toward applying physical scale cuts to HOS.