A

Euclid preparation

Astronomy and Astrophysics, vol. 713, pp. A212

Abstract

The Euclid satellite will measure spectroscopic redshifts for tens of millions of emission-line galaxies, allowing for one of the most precise tests of the cosmological model. In the context of Stage-IV surveys such as Euclid , the 3D clustering of galaxies plays a key role, providing both geometrical and dynamical cosmological constraints. In this paper, we conduct a comprehensive model comparison campaign for the multipole moments of the galaxy 2-point correlation function (2PCF) in redshift space. We tested state-of-the-art models, in particular the effective field theory of large-scale structure (EFT), a model based on the velocity difference generating function (VDG ∞ ), and variants of the Lagrangian perturbation theory (LPT), namely convolutional Lagrangian perturbation theory (CLPT) and convolutional Lagrangian effective field theory (CLEFT). We analysed the first three even multipole moments of the 2PCF in the Flagship 1 simulation of emission-line galaxies, which consists of four snapshots at z ∈ {0.9, 1.2, 1.5, 1.8} covering the redshift range of the Euclid spectroscopic sample. We studied template-fitting and full-shape approaches and compared the different models in terms of three performance metrics: reduced χ 2 , a figure of merit, and a figure of bias. We find that with the template-fitting approach, only the VDG ∞ model is able to reach a minimum fitting scale of s min = 20 h −1 Mpc at z = 0.9 without biasing the recovered parameters. Indeed, the EFT model becomes inaccurate already at s min = 30 h −1 Mpc. Conversely, in the full-shape analysis, the CLEFT and VDG ∞ models perform similarly well, but only the CLEFT model can reach s min = 20 h −1 Mpc, while the VDG ∞ model is unbiased down to s min = 25 h −1 Mpc at the lowest redshift. Overall, in order to achieve the accuracy required by Euclid , non-perturbative modelling, such as in the VDG ∞ or CLEFT models, should be considered. At the highest redshift probed by Euclid , the CLPT model is sufficient to describe the data with a high figure of merit. This comparison selects baseline models that perform best in ideal conditions and sets the stage for an optimal analysis of Euclid data in configuration space.

Authors 100

  1. Centre National de la Recherche Scientifique · Université de Toulon · University of Milan · Aix-Marseille Université · Centre de Physique Théorique

    Affiliation as printed

    Aix-Marseille Université, CNRS, CNES, LAM

    Aix-Marseille Université, Université de Toulon, CNRS, CPT

    Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano

  2. Centre National de la Recherche Scientifique · Université Paris Cité · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · Astrophysique, Instrumentation et Modélisation

    Affiliation as printed

    Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM

  3. Centre National de la Recherche Scientifique · Aix-Marseille Université

    Affiliation as printed

    Aix-Marseille Université, CNRS, CNES, LAM

  4. Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università di Genova

    INAF-Osservatorio Astronomico di Brera

    INFN-Sezione di Genova

  5. University of Bonn

    Affiliation as printed

    Universität Bonn, Argelander-Institut für Astronomie

  6. Institute of Space Sciences · Institut d'Estudis Espacials de Catalunya · Universitat Politècnica de Catalunya

    Affiliation as printed

    Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC

    Institute of Space Sciences (ICE, CSIC), Campus UAB

  7. Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  8. Scuola Internazionale Superiore di Studi Avanzati · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Fondazione ICSC Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing

    Affiliation as printed

    ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing

    INFN, Sezione di Trieste

    SISSA, International School for Advanced Studies

  9. Ikerbasque · Donostia International Physics Center

    Affiliation as printed

    Donostia International Physics Center (DIPC)

    IKERBASQUE, Basque Foundation for Science

  10. Scuola Internazionale Superiore di Studi Avanzati · Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    SISSA, International School for Advanced Studies

  11. Bielefeld University · Newcastle University

    Affiliation as printed

    Fakultät für Physik, Universität Bielefeld

    School of Mathematics, Statistics and Physics, Newcastle University

  12. University of Milan · Istituto Nazionale di Fisica Nucleare, Sezione di Milano

    Affiliation as printed

    Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano

    INFN-Sezione di Milano

  13. University of Geneva

    Affiliation as printed

    Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics

  14. Technion – Israel Institute of Technology

    Affiliation as printed

    Technion Israel Institute of Technology

  15. Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università di Genova

    INAF-Osservatorio Astronomico di Brera

    INFN-Sezione di Genova

  16. Institute of Space Sciences · Institut d'Estudis Espacials de Catalunya · Universitat Politècnica de Catalunya

    Affiliation as printed

    Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC

    Institute of Space Sciences (ICE, CSIC), Campus UAB

  17. Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia, Università di Bologna

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  18. Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Parma

    Affiliation as printed

    INFN Gruppo Collegato di Parma

  19. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  20. Centre National de la Recherche Scientifique · Laboratoire d'Annecy de Physique Théorique · Université Savoie Mont Blanc

    Affiliation as printed

    Laboratoire d’Annecy-le-Vieux de Physique Theorique, CNRS & Universite Savoie Mont Blanc

  21. Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  22. Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  23. Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Parma

    Affiliation as printed

    INFN Gruppo Collegato di Parma

  24. Brera Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Brera

  25. Royal Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory

  26. University of Bonn

    Affiliation as printed

    Universität Bonn, Argelander-Institut für Astronomie

  27. University of Bonn

    Affiliation as printed

    Universität Bonn, Argelander-Institut für Astronomie

  28. University of Oxford

    Affiliation as printed

    Department of Physics, Oxford University

  29. Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale

    Affiliation as printed

    Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale

  30. European Space Astronomy Centre

    Affiliation as printed

    ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo

  31. Heidelberg University

    Affiliation as printed

    Institut für Theoretische Physik, University of Heidelberg

  32. Brera Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Brera

  33. Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  34. Scuola Internazionale Superiore di Studi Avanzati · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

    SISSA, International School for Advanced Studies

  35. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia, Università di Bologna

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  36. Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  37. Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

  38. Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università di Genova

    INAF-Osservatorio Astronomico di Brera

    INFN-Sezione di Genova

  39. Astronomical Observatory of Capodimonte · University of Naples Federico II · National Institute for Astrophysics

    Affiliation as printed

    Department of Physics “E. Pancini”, University Federico II

    INAF-Osservatorio Astronomico di Capodimonte

  40. Istituto Nazionale di Fisica Nucleare, Sezione di Torino · Osservatorio Astrofisico di Torino · University of Turin · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università degli Studi di Torino

    INAF-Osservatorio Astrofisico di Torino

    INFN-Sezione di Torino

  41. Leiden University · Royal Observatory · Leiden Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory

    Leiden Observatory, Leiden University

  42. Osservatorio Astrofisico di Torino · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino

  43. National Institute for Astrophysics

    Affiliation as printed

    INAF-IASF Milano

  44. Astronomical Observatory of Rome · Istituto Nazionale di Fisica Nucleare, Sezione di Roma I · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

    INFN-Sezione di Roma, Piazzale Aldo Moro

  45. Universitat Autònoma de Barcelona · Port d'Informació Científica · Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas

    Affiliation as printed

    Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT)

    Port d’Informació Científica, Campus UAB

  46. Astronomical Observatory of Rome · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

  47. Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  48. Istituto Nazionale di Fisica Nucleare · Astronomical Observatory of Capodimonte · Istituto Nazionale di Fisica Nucleare, Sezione di Napoli · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Capodimonte

    INFN section of Naples

  49. University of Hawaiʻi at Mānoa · University of Hawaii System

    Affiliation as printed

    Institute for Astronomy, University of Hawaii

  50. University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna

  51. Instituto de Astrofísica de Canarias

    Affiliation as printed

    Instituto de Astrofísica de Canarias

  52. Royal Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory

  53. European Space Agency · European Space Astronomy Centre · European Space Research Institute

    Affiliation as printed

    ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo

    European Space Agency/ESRIN

  54. Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822

  55. Institució Catalana de Recerca i Estudis Avançats · Institute of Space Sciences · Consejo Superior de Investigaciones Científicas · Institut de Ciències del Cosmos · Universitat de Barcelona

    Affiliation as printed

    Institució Catalana de Recerca i Estudis Avançats (ICREA)

    Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans

    Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB)

  56. Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon

  57. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

  58. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  59. Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale

    Affiliation as printed

    Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale

  60. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

  61. European Space Astronomy Centre

    Affiliation as printed

    ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo

  62. Istituto Nazionale di Fisica Nucleare · Istituto Nazionale di Fisica Nucleare, Sezione di Padova

    Affiliation as printed

    INFN-Padova

  63. Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822

  64. Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  65. Institute for Space Astrophysics and Planetology · National Institute for Astrophysics

    Affiliation as printed

    INAF-Istituto di Astrofisica e Planetologia Spaziali

  66. Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  67. Astronomical Observatory of Rome · Agenzia Spaziale Italiana · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

    Space Science Data Center, Italian Space Agency

  68. Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822

  69. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Bologna

  70. Institute of Space Sciences · Institut d'Estudis Espacials de Catalunya · Universitat Politècnica de Catalunya

    Affiliation as printed

    Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC

    Institute of Space Sciences (ICE, CSIC), Campus UAB

  71. Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  72. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  73. Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  74. National Institute for Astrophysics

    Affiliation as printed

    INAF-IASF Milano

  75. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  76. Ludwig-Maximilians-Universität München

    Affiliation as printed

    University Observatory, LMU Faculty of Physics

  77. Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  78. Royal Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory

  79. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  80. Max Planck Institute for Extraterrestrial Physics

    Affiliation as printed

    Max Planck Institute for Extraterrestrial Physics

  81. Osservatorio Astronomico di Padova · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Padova

  82. Max Planck Institute for Extraterrestrial Physics · Ludwig-Maximilians-Universität München

    Affiliation as printed

    Max Planck Institute for Extraterrestrial Physics

    Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München

  83. University of Milan · Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Milano · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano

    INAF-Osservatorio Astronomico di Brera

    INFN-Sezione di Milano

  84. University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo

  85. Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology

  86. Affiliation as printed

    Felix Hormuth Engineering

  87. Technical University of Denmark

    Affiliation as printed

    Cosmic Dawn Center (DAWN)

    Technical University of Denmark

  88. Max Planck Institute for Astronomy

    Affiliation as printed

    Max-Planck-Institut für Astronomie

  89. Goddard Space Flight Center

    Affiliation as printed

    NASA Goddard Space Flight Center

  90. University College London

    Affiliation as printed

    Department of Physics and Astronomy, University College London

  91. University of Helsinki · Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki

  92. Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  93. Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology

  94. Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822

  95. Ludwig-Maximilians-Universität München

    Affiliation as printed

    Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München

  96. University of Geneva

    Affiliation as printed

    Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics

  97. University of Helsinki · Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics, P.O. Box 64, University of Helsinki

    Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki

  98. Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · Observatoire de Paris · Sorbonne Université · Laboratoire d'Étude de l'Univers et des Phénomènes Extrêmes

    Affiliation as printed

    Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS

  99. Osservatorio Astrofisico di Torino · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino

  100. University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo

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References 117