Euclid preparation

XLVII. Improving cosmological constraints using a new multi-tracer method with the spectroscopic and photometric samples

¹ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
² Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
³ School of Mathematics and Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK
⁴ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
⁵ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁶ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁷ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
⁸ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁹ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
¹⁰ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
¹¹ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy
¹² INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹³ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
¹⁴ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
¹⁵ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
¹⁶ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
¹⁷ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
¹⁸ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
¹⁹ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
²⁰ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
²¹ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
²² INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
²³ Dipartimento di Fisica e Astronomia “Augusto Righi” - Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
²⁴ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
²⁵ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
²⁶ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
²⁷ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
²⁸ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69100 Villeurbanne, France
²⁹ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
³⁰ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
³¹ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
³² Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciên- cias, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
³³ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
³⁴ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
³⁵ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
³⁶ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
³⁷ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
³⁸ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
³⁹ Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁴⁰ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁴¹ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁴² Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
⁴³ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA
⁴⁴ Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
⁴⁵ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁴⁶ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁴⁷ Cosmic Dawn Center (DAWN), Denmark
⁴⁸ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁴⁹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁵⁰ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁵¹ AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, 91191 Gif-sur-Yvette, France
⁵² Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
⁵³ Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
⁵⁴ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁵⁵ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands
⁵⁶ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁵⁷ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
⁵⁸ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁵⁹ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁶⁰ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁶¹ Dipartimento di Fisica e Astronomia “Augusto Righi” - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁶² Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road, DH1 3LE, UK
⁶³ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
⁶⁴ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁶⁵ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁶⁶ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁶⁷ School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, Newcastle-upon-Tyne, NE1 7RU, UK
⁶⁸ Department of Physics, Institute for Computational Cosmology, Durham University, South Road, DH1 3LE, UK
⁶⁹ Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁷⁰ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁷¹ Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁷² Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁷³ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁷⁴ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁷⁵ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov, 077125, Romania
⁷⁶ Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204, San Cristóbal de La Laguna, Tenerife, Spain
⁷⁷ Departamento de Astrofísica, Universidad de La Laguna, 38206, La Laguna, Tenerife, Spain
⁷⁸ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁷⁹ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁸⁰ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁸¹ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁸² Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
⁸³ Centro de Investigaciones Energéticas, Medioambientales y Tec- nológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁸⁴ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciên- cias, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁸⁵ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
⁸⁶ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
⁸⁷ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁸⁸ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁸⁹ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
⁹⁰ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
⁹¹ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin 69627 Villeurbanne Cedex, France
⁹² INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
⁹³ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁹⁴ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁹⁵ Junia, EPA department, 41 Bd Vauban, 59800 Lille, France
⁹⁶ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
⁹⁷ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
⁹⁸ ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
⁹⁹ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹⁰⁰ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
¹⁰¹ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
¹⁰² Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰³ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰⁴ Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹⁰⁵ Dipartimento di Fisica - Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹⁰⁶ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA
¹⁰⁷ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
¹⁰⁸ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
¹⁰⁹ Department of Physics & Astronomy, University of California Irvine, Irvine CA 92697, USA
¹¹⁰ Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia, B3H 3C3, Canada
¹¹¹ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹¹² Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹¹³ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
¹¹⁴ Department of Computer Science, Aalto University, PO Box 15400, Espoo 00 076, Finland
¹¹⁵ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹¹⁶ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53 Avenue des Martyrs, 38000 Grenoble, France
¹¹⁷ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Finland
¹¹⁸ Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹¹⁹ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹²⁰ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Victoria 3122, Australia
¹²¹ School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
¹²² Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
¹²³ ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil
¹²⁴ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm 106 91, Sweden
¹²⁵ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
¹²⁶ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹²⁷ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹²⁸ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹²⁹ Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma, Italy
¹³⁰ INFN, Sezione di Roma 2, Via della Ricerca Scientifica 1, Roma, Italy
¹³¹ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹³² Department of Astrophysics, University of Zurich, Winterthur-erstrasse 190, 8057 Zurich, Switzerland
¹³³ Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
¹³⁴ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515, 751 20 Uppsala, Sweden
¹³⁵ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
¹³⁶ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹³⁷ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹³⁸ Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA
¹³⁹ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010, New York, NY, USA

Received: 14 April 2024
Accepted: 8 July 2024

Abstract

Future data provided by the Euclid mission will allow us to better understand the cosmic history of the Universe. A metric of its performance is the figure-of-merit (FoM) of dark energy, usually estimated with Fisher forecasts. The expected FoM has previously been estimated taking into account the two main probes of Euclid, namely the three-dimensional clustering of the spectroscopic galaxy sample, and the so-called 3×2pt signal from the photometric sample (i.e., the weak lensing signal, the galaxy clustering, and their cross-correlation). So far, these two probes have been treated as independent. In this paper, we introduce a new observable given by the ratio of the (angular) two-point correlation function of galaxies from the two surveys. For identical (normalised) selection functions, this observable is unaffected by sampling noise, and its variance is solely controlled by Poisson noise. We present forecasts for Euclid where this multi-tracer method is applied and is particularly relevant because the two surveys will cover the same area of the sky. This method allows for the exploitation of the combination of the spectroscopic and photometric samples. When the correlation between this new observable and the other probes is not taken into account, a significant gain is obtained in the FoM, as well as in the constraints on other cosmological parameters. The benefit is more pronounced for a commonly investigated modified gravity model, namely the γ parametrisation of the growth factor. However, the correlation between the different probes is found to be significant and hence the actual gain is uncertain. We present various strategies for circumventing this issue and still extract useful information from the new observable.