A

Euclid preparation

Astronomy and Astrophysics, vol. 713, pp. A213

Abstract

The extraction of cosmological information from two-point statistics critically relies on the assumed form of their likelihood. Although a Gaussian likelihood is generally adopted, the first paper of this series showed that the distribution of power-spectrum estimates exhibits non-Gaussian features on both large and small scales ( k < 0.5 h /Mpc), with their amplitudes depending on the survey volume, masking, and shot noise. In this work, we account for this skewness in parameter inference by modelling the likelihood through an Edgeworth expansion. This procedure involves the complete skewness tensor, composed of one-point, two-point, and three-point correlators. To simplify the calculations of this expansion, we performed a change in the basis, which reduced the precision matrix to the identity. In this basis, the off-diagonal elements of the skewness tensor are consistent with zero, while the amplitude of its diagonal match the level expected for a Gaussian underlying field. We performed a parameter inference with this likelihood model and found that including only the diagonal part of the skewness is sufficient; whereas incorporating the full skewness tensor injects noise without improving accuracy. Despite the estimated excess skewness in the original basis, the cosmological constraints remain effectively unchanged when adopting a Gaussian likelihood or considering the more complete Edgeworth expansion, with variations in the figure of merit of cosmological parameters between the two cases below 5%. This result remains unchanged against variations of the survey volume and geometry, scale-cut, as well as the two-point statistics (i.e. power spectrum or correlation function). Using 10 000 cloned Euclid large mocks based on realistic galaxy catalogues with characteristics approximating future Euclid data, we found no detectable excess skewness on intermediate scales, due to the level of shot noise expected for the Euclid spectroscopic sample. We conclude that the Gaussian likelihood assumption is robust for Euclid two-point statistics analyses in both Fourier and the configuration space.

Authors 100

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

    Affiliation as printed

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

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

  2. Centre National de la Recherche Scientifique · Aix-Marseille Université · Université de Toulon · Centre de Physique Théorique

    Affiliation as printed

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

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

    Affiliation as printed

    Aix Marseille Univ, INSERM, MMG

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  4. National Institute for Astrophysics

    Affiliation as printed

    INAF-IASF Milano

  5. European Space Agency · European Space Astronomy Centre

    Affiliation as printed

    ESAC/ESA

  6. National Institute for Astrophysics · Brera Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Brera

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

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

    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

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

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  12. Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique de Paris · Sorbonne Université · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Institut de Physique Théorique

    Affiliation as printed

    Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay

    Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université

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

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

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

    Affiliation as printed

    Dipartimento di Fisica, Università di Genova

    INAF-Osservatorio Astronomico di Brera

    INFN-Sezione di Genova

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

    Affiliation as printed

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

    INAF-Osservatorio Astronomico di Capodimonte

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

    Affiliation as printed

    Dipartimento di Fisica, Università degli Studi di Torino

    INAF-Osservatorio Astrofisico di Torino

    INFN-Sezione di Torino

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

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill

    Leiden Observatory, Leiden University

  18. National Institute for Astrophysics · Osservatorio Astrofisico di Torino

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino

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

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

    INFN-Sezione di Roma,Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi

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

    Affiliation as printed

    Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT)

    Port d’Informació Científica, Campus UAB

  21. RWTH Aachen University · Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

    Affiliation as printed

    Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR), Linder Höhe

    Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University

  22. National Institute for Astrophysics · Astronomical Observatory of Rome

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

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

    Affiliation as printed

    INAF-Osservatorio Astronomico di Capodimonte

    INFN section of Naples

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

    Affiliation as printed

    Institute for Astronomy, University of Hawaii

  26. Instituto de Astrofísica de Canarias

    Affiliation as printed

    Instituto de Astrofísica de Canarias

  27. University of Edinburgh · Royal Observatory

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill

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

    Affiliation as printed

    ESAC/ESA

    European Space Agency/ESRIN, Largo Galileo Galilei 1

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

    Affiliation as printed

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

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

    Affiliation as printed

    Institució Catalana de Recerca i Estudis Avançats (ICREA)

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

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

  31. 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

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

    Affiliation as printed

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

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

  33. University of Lisbon · Institute of Astrophysics and Space Sciences

    Affiliation as printed

    Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande

    Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa,Campo Grande

  34. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

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

    Affiliation as printed

    Aix-Marseille Université, CNRS, CNES, LAM

  36. National Institute for Astrophysics · Trieste Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

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

    Affiliation as printed

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

  38. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

  39. European Space Agency · European Space Astronomy Centre

    Affiliation as printed

    ESAC/ESA

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

    Affiliation as printed

    INFN-Padova

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

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

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

    Affiliation as printed

    INAF-Istituto di Astrofisica e Planetologia Spaziali

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

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

    Affiliation as printed

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

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

    Affiliation as printed

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

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Bologna

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

    Affiliation as printed

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

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

  48. University of Bristol

    Affiliation as printed

    School of Physics, HH Wills Physics Laboratory, University of Bristol

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

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  50. National Institute for Astrophysics · Trieste Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  52. National Institute for Astrophysics

    Affiliation as printed

    INAF-IASF Milano

  53. National Institute for Astrophysics · Trieste Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  54. Ludwig-Maximilians-Universität München

    Affiliation as printed

    University Observatory, LMU Faculty of Physics

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

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  56. University of Edinburgh · Royal Observatory

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  58. Max Planck Institute for Extraterrestrial Physics

    Affiliation as printed

    Max Planck Institute for Extraterrestrial Physics

  59. National Institute for Astrophysics · Osservatorio Astronomico di Padova

    Affiliation as printed

    INAF-Osservatorio Astronomico di Padova

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

    Affiliation as printed

    Max Planck Institute for Extraterrestrial Physics

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

  61. University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo

  62. Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology

  63. Technical University of Denmark

    Affiliation as printed

    Cosmic Dawn Center (DAWN)

    Technical University of Denmark

  64. Max Planck Institute for Astronomy

    Affiliation as printed

    Max-Planck-Institut für Astronomie

  65. University College London

    Affiliation as printed

    Department of Physics and Astronomy, University College London

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

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  67. Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology

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

    Affiliation as printed

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

  69. University of Geneva

    Affiliation as printed

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

  70. Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics

    Helsinki Institute of Physics

  71. Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · Sorbonne Université · Observatoire de Paris · 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

  72. National Institute for Astrophysics · Osservatorio Astrofisico di Torino

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino

  73. University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo

  74. Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics

    Helsinki Institute of Physics

  75. SKA Observatory

    Affiliation as printed

    SKAO, Jodrell Bank, Lower Withington

  76. Centre National de la Recherche Scientifique · Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules

    Affiliation as printed

    Centre de Calcul de l’IN2P3/CNRS

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  78. National Institute for Astrophysics · Trieste Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  79. FHNW University of Applied Sciences and Arts Northwestern Switzerland

    Affiliation as printed

    University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science

  80. University of Bonn

    Affiliation as printed

    Universität Bonn, Argelander-Institut für Astronomie

  81. Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology

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

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

    INFN-Sezione di Roma,Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi

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

    Affiliation as printed

    Aix-Marseille Université, CNRS, CNES, LAM

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

  85. Durham University

    Affiliation as printed

    Department of Physics, Institute for Computational Cosmology, Durham University

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  87. Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Université Paris Cité · Centre Pierre Binétruy

    Affiliation as printed

    CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3

    Université Paris Cité, CNRS, Astroparticule et Cosmologie

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  89. National Institute for Astrophysics · Astronomical Observatory of Rome

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

  90. École Polytechnique Fédérale de Lausanne

    Affiliation as printed

    Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny

  91. European Space Agency

    Affiliation as printed

    Telespazio UK S.L. for European Space Agency (ESA)

  92. 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

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

  94. University of Bonn

    Affiliation as printed

    Universität Bonn, Argelander-Institut für Astronomie

  95. Universitat Autònoma de Barcelona · Institute for High Energy Physics · Barcelona Institute of Science and Technology · Port d'Informació Científica

    Affiliation as printed

    Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB

    Port d’Informació Científica, Campus UAB

  96. European Space Agency · European Space Research and Technology Centre

    Affiliation as printed

    European Space Agency/ESTEC

  97. Institute for High Energy Physics · Barcelona Institute of Science and Technology

    Affiliation as printed

    Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB

  98. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

  99. National Institute for Astrophysics · Trieste Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  100. University of Copenhagen

    Affiliation as printed

    DARK, Niels Bohr Institute, University of Copenhagen

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