<i>Euclid</i> preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

  • M Knabenhans
    Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
  • J Stadel
    Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
  • D Potter
    Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
  • J Dakin
    Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
  • S Hannestad
    Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
  • T Tram
    Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
  • S Marelli
    Chair of Risk, Safety and Uncertainty Quantification, Department of Civil Engineering, ETH Zurich, Stefano-Franscini-Platz 5, CH-8093 Zurich, Switzerland
  • A Schneider
    Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
  • R Teyssier
    Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
  • P Fosalba
    Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193 Barcelona, Spain
  • S Andreon
    INAF-Osservatorio Astronomico di Brera, Via Brera 28, I-20122 Milano, Italy
  • N Auricchio
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • C Baccigalupi
    SISSA, International School for Advanced Studies, Via Bonomea 265, I-34136 Trieste TS, Italy
  • A Balaguera-Antolínez
    Universidad de la Laguna, E-38206 San Cristóbal de La Laguna, Tenerife, Spain
  • M Baldi
    Istituto Nazionale di Astrofisica (INAF) - Osservatorio di Astrofisica e Scienza dello Spazio (OAS), Via Gobetti 93/3, I-40127 Bologna, Italy
  • S Bardelli
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • P Battaglia
    INAF-IASF Bologna, Via Piero Gobetti 101, I-40129 Bologna, Italy
  • R Bender
    Fakultät für Physik, Universitäts-Sternwarte München, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, D-81679 München, Germany
  • A Biviano
    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
  • C Bodendorf
    Max Planck Institute for Extraterrestrial Physics, Giessenbachstr 1, D-85748 Garching, Germany
  • E Bozzo
    Department of Astronomy, University of Geneva, ch. d’Écogia 16, CH-1290 Versoix, Switzerland
  • E Branchini
    INFN-Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Roma, Italy
  • M Brescia
    INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy
  • C Burigana
    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
  • R Cabanac
    Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, F-31400 Toulouse, France
  • S Camera
    INFN-Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
  • V Capobianco
    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, I-10025 Pino Torinese (TO), Italy
  • A Cappi
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • C Carbone
    INAF-IASF Milano, Via Alfonso Corti 12, I-20133 Milano, Italy
  • J Carretero
    Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain
  • C S Carvalho
    Faculdade de Ciências, Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa, Tapada da Ajuda, P-1349-018 Lisboa, Portugal
  • R Casas
    Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193 Barcelona, Spain
  • S Casas
    AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France
  • M Castellano
    INAF-Osservatorio Astronomico di Roma, Via Frascati 33, I-00078 Monteporzio Catone, Italy
  • G Castignani
    Observatoire de Sauverny, Ecole Polytechnique Fédérale de Lau- sanne, CH-1290 Versoix, Switzerland
  • S Cavuoti
    INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy
  • R Cledassou
    Centre National d’Etudes Spatiales, Toulouse, France
  • C Colodro-Conde
    Instituto de Astrofísica de Canarias, Calle Vía Làctea s/n, E-38204 San Cristóbal de la Laguna, Tenerife, Spain
  • G Congedo
    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
  • C J Conselice
    University of Nottingham, University Park, Nottingham NG7 2RD, UK
  • L Conversi
    European Space Agency/ESRIN, Largo Galileo Galilei 1, I-00044 Frascati, Roma, Italy
  • Y Copin
    Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, F-69622 Villeurbanne, France
  • L Corcione
    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, I-10025 Pino Torinese (TO), Italy
  • J Coupon
    Department of Astronomy, University of Geneva, ch. d’Écogia 16, CH-1290 Versoix, Switzerland
  • H M Courtois
    University of Lyon, UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, France
  • A Da Silva
    Faculdade de Ciências, Departamento de Física, Universidade de Lisboa, Edifício C8, Campo Grande, P-1749-016 Lisboa, Portugal
  • S de la Torre
    Aix-Marseille Univ, CNRS, CNES, LAM, Marseille, France
  • D Di Ferdinando
    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
  • C A J Duncan
    Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
  • X Dupac
    ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, E-28692 Villanueva de la Cañada, Madrid, Spain
  • G Fabbian
    Department of Physics & Astronomy, University of Sussex, Brighton BN1 9QH, UK
  • S Farrens
    AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France
  • P G Ferreira
    Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
  • F Finelli
    Istituto Nazionale di Astrofisica (INAF) - Osservatorio di Astrofisica e Scienza dello Spazio (OAS), Via Gobetti 93/3, I-40127 Bologna, Italy
  • M Frailis
    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
  • E Franceschi
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • S Galeotta
    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
  • B Garilli
    INAF-IASF Milano, Via Alfonso Corti 12, I-20133 Milano, Italy
  • C Giocoli
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • G Gozaliasl
    Department of Physics, University of Helsinki, PO Box 64, FI-00014 Helsinki, Finland
  • J Graciá-Carpio
    Max Planck Institute for Extraterrestrial Physics, Giessenbachstr 1, D-85748 Garching, Germany
  • F Grupp
    Fakultät für Physik, Universitäts-Sternwarte München, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, D-81679 München, Germany
  • L Guzzo
    INAF-Osservatorio Astronomico di Brera, Via Brera 28, I-20122 Milano, Italy
  • W Holmes
    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
  • F Hormuth
    von Hoerner & Sulger GmbH, SchloßPlatz 8, D-68723 Schwetzingen, Germany
  • H Israel
    Fakultät für Physik, Universitäts-Sternwarte München, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, D-81679 München, Germany
  • K Jahnke
    Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
  • E Keihanen
    Department of Physics and Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin katu 2, FI-00014 Helsinki, Finland
  • S Kermiche
    Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
  • C C Kirkpatrick
    Department of Physics and Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin katu 2, FI-00014 Helsinki, Finland
  • B Kubik
    Institut de Physique Nucléaire de Lyon, 4, rue Enrico Fermi, F-69622 Villeurbanne cedex, France
  • M Kunz
    Département de Physique Théorique and Centre for Astroparticle Physics, Université de Genève, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
  • H Kurki-Suonio
    Department of Physics and Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin katu 2, FI-00014 Helsinki, Finland
  • S Ligori
    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, I-10025 Pino Torinese (TO), Italy
  • P B Lilje
    Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, N-0315 Oslo, Norway
  • I Lloro
    NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, NL-7991PD Dwingeloo, the Netherlands
  • D Maino
    INAF-IASF Milano, Via Alfonso Corti 12, I-20133 Milano, Italy
  • O Marggraf
    Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany
  • K Markovic
    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
  • N Martinet
    Aix-Marseille Univ, CNRS, CNES, LAM, Marseille, France
  • F Marulli
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • R Massey
    Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
  • N Mauri
    Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy
  • S Maurogordato
    Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, F-06304 Nice cedex 4, France
  • E Medinaceli
    INAF-IASF Bologna, Via Piero Gobetti 101, I-40129 Bologna, Italy
  • M Meneghetti
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • B Metcalf
    Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy
  • G Meylan
    Observatoire de Sauverny, Ecole Polytechnique Fédérale de Lau- sanne, CH-1290 Versoix, Switzerland
  • M Moresco
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • B Morin
    AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France
  • L Moscardini
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • E Munari
    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
  • C Neissner
    Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain
  • S M Niemi
    Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
  • C Padilla
    Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain
  • S Paltani
    Department of Astronomy, University of Geneva, ch. d’Écogia 16, CH-1290 Versoix, Switzerland
  • F Pasian
    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
  • L Patrizii
    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
  • V Pettorino
    AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France
  • S Pires
    AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France
  • G Polenta
    Space Science Data Center, Italian Space Agency, via del Politecnico snc, I-00133 Roma, Italy
  • M Poncet
    Centre National d’Etudes Spatiales, Toulouse, France
  • F Raison
    Max Planck Institute for Extraterrestrial Physics, Giessenbachstr 1, D-85748 Garching, Germany
  • A Renzi
    INFN-Padova, Via Marzolo 8, I-35131 Padova, Italy
  • J Rhodes
    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
  • G Riccio
    INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy
  • E Romelli
    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
  • M Roncarelli
    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
  • R Saglia
    Fakultät für Physik, Universitäts-Sternwarte München, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, D-81679 München, Germany
  • A G Sánchez
    Max Planck Institute for Extraterrestrial Physics, Giessenbachstr 1, D-85748 Garching, Germany
  • D Sapone
    Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
  • P Schneider
    Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany
  • V Scottez
    Institut d’Astrophysique de Paris, 98bis Boulevard Arago, F-75014 Paris, France
  • A Secroun
    Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
  • S Serrano
    Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193 Barcelona, Spain
  • C Sirignano
    INFN-Padova, Via Marzolo 8, I-35131 Padova, Italy
  • G Sirri
    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
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    INFN-Padova, Via Marzolo 8, I-35131 Padova, Italy
  • F Sureau
    AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France
  • P Tallada Crespí
    Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, E-28040 Madrid, Spain
  • A N Taylor
    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
  • M Tenti
    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
  • I Tereno
    Faculdade de Ciências, Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa, Tapada da Ajuda, P-1349-018 Lisboa, Portugal
  • R Toledo-Moreo
    Departamento de Electrónica y Tecnología de Computadoras, Universidad Politécnica de Cartagena, E-30202 Cartagena, Spain
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    Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, E-28040 Madrid, Spain
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    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
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    Department of Physics, University of Helsinki, PO Box 64, FI-00014 Helsinki, Finland
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    Fakultät für Physik, Universitäts-Sternwarte München, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, D-81679 München, Germany
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    SISSA, International School for Advanced Studies, Via Bonomea 265, I-34136 Trieste TS, Italy
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    Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
  • N Welikala
    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
  • L Whittaker
    Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
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    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
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    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy

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<jats:title>ABSTRACT</jats:title> <jats:p>We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent level accurate emulation is now supported in the eight-dimensional parameter space of w0waCDM+∑mν models between redshift z = 0 and z = 3 for spatial scales within the range $0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy, and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 30003 particles in boxes of 1(h−1 Gpc)3 volumes based on paired-and-fixed initial conditions, and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter wa significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors such as HALOFIT, HMCode, and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of $1{{\ \rm per\ cent}}$ or better for $0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$ and z ≤ 3 compared to high-resolution dark-matter-only simulations. EuclidEmulator2 is publicly available at https://github.com/miknab/EuclidEmulator2.</jats:p>

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