Euclid: Optimising tomographic redshift binning for 3 × 2 pt power spectrum constraints on dark energy^★

¹ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
² School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
³ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
⁴ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
⁵ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
⁶ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
⁷ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
⁸ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
⁹ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹⁰ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
¹¹ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
¹² Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹³ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹⁴ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
¹⁵ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
¹⁶ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
¹⁷ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
¹⁸ Faculdade de Ciências da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal
¹⁹ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
²⁰ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
²¹ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
²² INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
²³ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
²⁴ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
²⁵ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
²⁶ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
²⁷ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
²⁸ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
²⁹ Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204 San Cristóbal de La Laguna, Tenerife, Spain
³⁰ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³¹ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
³² ESAC/ESA, Camino Bajo del Castillo s/n, Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
³³ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
³⁴ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
³⁵ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
³⁶ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
³⁷ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
³⁸ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
³⁹ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁴⁰ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁴¹ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁴² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁴³ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁴⁴ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁴⁵ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁴⁶ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁴⁷ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁴⁸ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁴⁹ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern 0315, Oslo, Norway
⁵⁰ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁵¹ Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
⁵² Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁵³ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁵⁴ Cosmic Dawn Center (DAWN), Denmark
⁵⁵ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
⁵⁶ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁵⁷ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁵⁸ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁵⁹ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁶⁰ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁶¹ Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
⁶² Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁶³ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD, Dwingeloo, The Netherlands
⁶⁴ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁶⁵ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁶⁶ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
⁶⁷ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁶⁸ Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
⁶⁹ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁷⁰ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁷¹ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁷² Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁷³ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁷⁴ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁷⁵ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands
⁷⁶ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁷⁷ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁷⁸ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
⁷⁹ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁸⁰ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁸¹ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁸² Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada, 2008 Santiago, Chile
⁸³ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁸⁴ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁸⁵ Satlantis, University Science Park, Sede Bld, 48940 Leioa-Bilbao, Spain
⁸⁶ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain
⁸⁷ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁸⁸ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
⁸⁹ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁹⁰ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands
⁹¹ Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
⁹² Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁹³ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
⁹⁴ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus (Aosta Valley), Italy
⁹⁵ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
⁹⁶ Department of Physics, Royal Holloway, University of London, TW20 0EX, UK
⁹⁷ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy

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Received: 13 January 2025
Accepted: 2 February 2026

Abstract

The tomographic approach to analysing the 3 × 2 pt signal involves dividing the observed galaxy sample into a configuration of redshift bins. We present a simulation-based method to explore the optimum tomographic binning strategy for Euclid, focussing on the expected configuration of its first major data release (DR1). To do so, we 1) simulated a Euclid-like observation and generated mock shear catalogues from multiple realisations of the 3 × 2 pt fields on the sky; and 2) measured the 3 × 2 pt Pseudo-C_ℓ power spectra for a given tomographic configuration and derived the constraints they place on the standard dark energy equation-of-state parameters, (w₀, w_a). For a simulation including Gaussian-distributed photometric redshift uncertainties and shape noise under a ΛCDM cosmology, we find that bins that are equipopulated with galaxies yield the best constraints on (w₀, w_a) for an analysis of the full 3 × 2 pt signal or the angular clustering component only. For the cosmic shear component, the optimum (w₀, w_a) constraints can be achieved by bins equally spaced in fiducial comoving distance. However, the advantage with respect to alternative binning choices is only of a few per cent in the size of the 1σ (w₀, w_a) contour and we conclude that the cosmic shear is relatively insensitive to the binning methodology. We find that the information gain extracted on (w₀, w_a) for any 3 × 2 pt component starts to become saturated beyond roughly seven or eight bins. Any marginal gains resulting from a greater number of bins are likely to be limited by additional uncertainties present in a real measurement and the increasing demand for accuracy of the covariance matrix. Finally, we considered a 5% contamination from catastrophic photometric redshift outliers and found that if these errors are not mitigated in the analysis, the bias induced in the 3 × 2 pt signal for ten equipopulated bins results in dark energy constraints that are inconsistent with the fiducial ΛCDM cosmology at ≳3σ.